wikipedia_id stringlengths 2 8 | wikipedia_title stringlengths 1 243 | url stringlengths 44 370 | contents stringlengths 53 2.22k | id int64 0 6.14M |
|---|---|---|---|---|
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
9, and received a few lessons from Zelodec. By the late 1920s, in his early teenage years, he was a working musician, playing for community events. In the 1930s, he formed a business relationship with Joe Trolli and began making radio appearances on stations such as WJAY and WGAR. As his reputation spr... | 31,500 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
opened a tavern, calling it the Yankovic Bar. It became a popular hangout for local musicians, and he continued to run it until he sold it in 1948, dedicating himself to the accordion.
Yankovic enlisted in the armed forces in 1943, and cut numerous records while on leave, prior to his departure for Eu... | 31,501 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
and four other musicians were assigned to special services to entertain the troops, including General George Patton and his Third United States Army.
Yankovic hit the national scene when he earned two platinum singles for "Just Because" (1947) and "Blue Skirt Waltz" (1949). Others who recorded the Blu... | 31,502 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
the melody. Parrish changed "red" to "blue". Yankovic sold over 2.5 million records and with the Tunemixers version and Guy Lombardo's version, it sold over 4 million records total in 1949. It was the second Cleveland-style song to sell over one million recordings.
Columbia Records initially refused t... | 31,503 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
Milwaukee at the Milwaukee Arena on June 9, 1948.
In 1970, a house fire destroyed the gold records for "Just Because" and "Blue Skirt Waltz".
Yankovic also hosted the television series "Polka Time" for Buffalo, New York-based WKBW-TV for 26 weeks in 1962. He commuted from Cleveland to host each episo... | 31,504 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
polka music among many other styles, has jokingly hypothesized that he was given accordion lessons as a child because his parents thought that "there should be at least one more accordion-playing Yankovic in the world." Al performed accordion on "Who Stole the Kishka?" on one of Frankie's final records... | 31,505 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
his loyal fans and fellow musicians attended his memorial service. At his peak, Yankovic traveled extensively and performed 325 shows a year. He sold 30 million records during his lifetime.
# Hometown square named in his honor.
In Bob Dolgan's 2006 biography of Yankovic, Frankie's longtime drummer Da... | 31,506 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
Former band members.
- Denny Boneck (Milwaukee, WI), stand-up bass and back-up vocals. Played, toured and recorded with Frank as one of the "Yanks" from 1970 to 1981.
- Joseph A. Godec upright 3/4 bass player and Frank Godec guitar toured Ely and range 1940-44 and 1951.
- Johnny Pecon - Button Box a... | 31,507 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
Las Vegas, and top nightclubs in the United States. Tops played second accordion with Frank's band.
- Georgie Cook - Banjo player, who helped Yankovic establish the "Cleveland Sound".
- Joey Miskulin - Began playing with Yankovic in 1962 at the age of 13. This was the start of a relationship that las... | 31,508 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
Bell - played bass with Yankovic. His father was a tenor in the Slovenian operettas in Cleveland
- Steve Kucenski - played 2nd accordion in the late 70s to early 90s.
- Adolph "Church" Srnick - long time bass player with Yankovic. Played the stand up 3/4" bass and also the baby "electric" bass from 1... | 31,509 |
43727 | Frankie Yankovic | https://en.wikipedia.org/w/index.php?title=Frankie%20Yankovic | Frankie Yankovic
vic, which was written at first as a commercial for the TV show.
# See also.
- Slovene Americans
# Further reading.
- Dolgan, Bob (2006). "America's Polka King: The Real Story of Frankie Yankovic". Cleveland, OH: Gray & Company, Publishers.
# External links.
- Sample text from the book "America's... | 31,510 |
43742 | 287 | https://en.wikipedia.org/w/index.php?title=287 | 287
287
Year 287 (CCLXXXVII) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Valerius and Valerius (or, less frequently, year 1040 "Ab urbe condita"). The denomination 287 for this year has been used since t... | 31,511 |
43742 | 287 | https://en.wikipedia.org/w/index.php?title=287 | 287
has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.
# Events.
onlyinclude
## By place.
### Roman Empire.
- Emperor Diocletian and Maximian become Roman Consuls.
- Diocletian signs a peace treaty with Bahram II, king of Persia... | 31,512 |
43743 | 283 | https://en.wikipedia.org/w/index.php?title=283 | 283
283
Year 283 (CCLXXXIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Carus and Carinus (or, less frequently, year 1036 "Ab urbe condita"). The denomination 283 for this year has been used since the ear... | 31,513 |
43743 | 283 | https://en.wikipedia.org/w/index.php?title=283 | 283
Carus receives for his victories in Persia the title of "Persicus Maximus".
- Carus dies in mysterious circumstances during the war against the Sassanids; during a violent dust storm he is killed by a stroke of lightning.
- Marcus Aurelius Carinus succeeds his father Carus.
- December – Numerian is proclaimed Em... | 31,514 |
43743 | 283 | https://en.wikipedia.org/w/index.php?title=283 | 283
ves for his victories in Persia the title of "Persicus Maximus".
- Carus dies in mysterious circumstances during the war against the Sassanids; during a violent dust storm he is killed by a stroke of lightning.
- Marcus Aurelius Carinus succeeds his father Carus.
- December – Numerian is proclaimed Emperor by hi... | 31,515 |
43745 | 281 | https://en.wikipedia.org/w/index.php?title=281 | 281
281
Year 281 (CCLXXXI) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Tiberianus (or, less frequently, year 1034 "Ab urbe condita"). The denomination 281 for this year has been used since the... | 31,516 |
43745 | 281 | https://en.wikipedia.org/w/index.php?title=281 | 281
ommon year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Tiberianus (or, less frequently, year 1034 "Ab urbe condita"). The denomination 281 for this year has been used since the early medieval period, when th... | 31,517 |
43744 | 282 | https://en.wikipedia.org/w/index.php?title=282 | 282
282
Year 282 (CCLXXXII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Victorinus (or, less frequently, year 1035 "Ab urbe condita"). The denomination 282 for this year has been used since the ... | 31,518 |
43744 | 282 | https://en.wikipedia.org/w/index.php?title=282 | 282
an Illyrian and praetorian prefect, is proclaimed new emperor.
- Carus defeats the Quadi and Sarmatians on the Danube; for his victories he is given the title "Germanicus Maximus".
- Carus appoints his oldest son Marcus Aurelius Carinus, "Caesar" and co-emperor of the western Roman Empire.
### China.
- A new ci... | 31,519 |
43744 | 282 | https://en.wikipedia.org/w/index.php?title=282 | 282
and praetorian prefect, is proclaimed new emperor.
- Carus defeats the Quadi and Sarmatians on the Danube; for his victories he is given the title "Germanicus Maximus".
- Carus appoints his oldest son Marcus Aurelius Carinus, "Caesar" and co-emperor of the western Roman Empire.
### China.
- A new city is constr... | 31,520 |
43746 | 280 | https://en.wikipedia.org/w/index.php?title=280 | 280
280
Year 280 (CCLXXX) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Messalla and Gratus (or, less frequently, year 1033 "Ab urbe condita"). The denomination 280 for this year has been used since the earl... | 31,521 |
43746 | 280 | https://en.wikipedia.org/w/index.php?title=280 | 280
Germans destroy the Roman fleet on the Rhine; Bonosus is proclaimed emperor at Colonia Agrippina (Cologne).
- Probus defeats the army under Bonosus. Bonosus sees no way out and hangs himself. His family is treated with honours.
- Julius Saturninus, governor of Syria, is in Alexandria, charged with the defense of ... | 31,522 |
43746 | 280 | https://en.wikipedia.org/w/index.php?title=280 | 280
completes the unification of China, which was previously divided between three contending powers during the Three Kingdoms period. The Jin dynasty's capital of Luoyang becomes a thriving centre of commerce as foreign diplomats and traders travel there.
### Persia.
- King Bahram II of the Sassanid Empire (Persia) ... | 31,523 |
43746 | 280 | https://en.wikipedia.org/w/index.php?title=280 | 280
uoyang becomes a thriving centre of commerce as foreign diplomats and traders travel there.
### Persia.
- King Bahram II of the Sassanid Empire (Persia) sends envoys to seek peaceful relations with Rome.
### India.
- The Gupta Empire (India) is founded (approximate date).
## By topic.
### Arts and sciences.
... | 31,524 |
43747 | 279 | https://en.wikipedia.org/w/index.php?title=279 | 279
279
Year 279 (CCLXXIX) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Paternus (or, less frequently, year 1032 "Ab urbe condita"). The denomination 279 for this year has been used since the ... | 31,525 |
43747 | 279 | https://en.wikipedia.org/w/index.php?title=279 | 279
the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.
# Events.
onlyinclude
## By place.
### Roman Empire.
- Emperor Probus defeats the Burgundians and Vandals in Raetia and Pannonia (modern Switzerland and Hungary).
### China.
- Winter – Conques... | 31,526 |
43748 | 274 | https://en.wikipedia.org/w/index.php?title=274 | 274
274
Year 274 (CCLXXIV) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Aurelianus and Capitolinus (or, less frequently, year 1027 "Ab urbe condita"). The denomination 274 for this year has been used sinc... | 31,527 |
43748 | 274 | https://en.wikipedia.org/w/index.php?title=274 | 274
Empire, the Roman Empire is united again.
- Rome greets Aurelian as "Restitutor Orbis" ("Restorer of the World") and accords him a magnificent triumph (victory procession), which is graced by his captives Tetricus I and his son Tetricus II.
- Aurelian issues an important reform of Roman currency.
- Germanic trib... | 31,528 |
43748 | 274 | https://en.wikipedia.org/w/index.php?title=274 | 274
of the Sun. This religion, which is in essence monotheistic, becomes the state religion of Rome.
- Britain rebels over the value of coinage.
### Africa.
- The Kingdom of Aksum attains great prosperity thanks to its control of Red Sea trade.
## By topic.
### Religion.
- March 2 – Mani, a sage of Persia, dies a... | 31,529 |
43748 | 274 | https://en.wikipedia.org/w/index.php?title=274 | 274
from Byzantine and Roman Emperors.
- December 30 – Pope Felix I dies in Rome after a 5-year reign.
### Transportation.
- Japanese shipwrights build a 100-foot oar-powered vessel for Emperor Ōjin. The Japanese will not use sails for another seven centuries.
/onlyinclude
# Births.
- Li Xiong, first emperor of C... | 31,530 |
43750 | 273 | https://en.wikipedia.org/w/index.php?title=273 | 273
273
Year 273 (CCLXXIII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Tacitus and Placidianus (or, less frequently, year 1026 "Ab urbe condita"). The denomination 273 for this year has been used since... | 31,531 |
43750 | 273 | https://en.wikipedia.org/w/index.php?title=273 | 273
Marcus Claudius Tacitus, future Roman Emperor, is consul in Rome.
- Tetricus I and Tetricus II are deposed as Gallic Emperors by Aurelian.
- Administrative reorganization of Italy: Aurelian adopts as permanent the reforms instituted by Caracalla.
- Aurelian increases Rome's daily bread ration to nearly 1.5 pound... | 31,532 |
43750 | 273 | https://en.wikipedia.org/w/index.php?title=273 | 273
d adds pig fat to the list of foods distributed free to the populace.
- Cassius Longinus, counselor of queen Zenobia, is executed by the Romans for conspiring against Aurelian.
- An Indian delegation visits Aurelian.
### Persia.
- King Hormizd I of Persia dies after a brief reign in which he has shown tolerance... | 31,533 |
43751 | 272 | https://en.wikipedia.org/w/index.php?title=272 | 272
272
Year 272 (CCLXXII) was a leap year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Postumius and Veldumnianus (or, less frequently, year 1025 "Ab urbe condita"). The denomination 272 for this year has been used since th... | 31,534 |
43751 | 272 | https://en.wikipedia.org/w/index.php?title=272 | 272
Aurelian defeats the forces of the Palmyrene Empire near Antioch. Queen Zenobia flees under cover of darkness to Emesa (Syria).
- Battle of Emesa: Aurelian destroys the Palmyrene heavy cavalry ("clibanarii") and conquers Palmyra. Zenobia escapes to Persia but is captured on the Euphrates.
- Aurelian lays siege to... | 31,535 |
43751 | 272 | https://en.wikipedia.org/w/index.php?title=272 | 272
Religion.
- Dometius succeeds Titus as Patriarch of Constantinople.
- Saint Denis, first Bishop of Paris, and two of his disciples are beheaded on the road to the Temple of Mercury that stands atop a hill outside of the city. The hill will later be called Montmartre (Mountain of Martyrs) in Lutetia (modern Paris)... | 31,536 |
43751 | 272 | https://en.wikipedia.org/w/index.php?title=272 | 272
the Temple of Mercury that stands atop a hill outside of the city. The hill will later be called Montmartre (Mountain of Martyrs) in Lutetia (modern Paris).
- Paul of Samosata is deposed as Patriarch of Antioch.
/onlyinclude
# Births.
- February 27 – Constantine the Great, first Christian Emperor of the Roman E... | 31,537 |
43752 | 277 | https://en.wikipedia.org/w/index.php?title=277 | 277
277
Year 277 (CCLXXVII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Paulinus (or, less frequently, year 1030 "Ab urbe condita"). The denomination 277 for this year has been used since the ea... | 31,538 |
43752 | 277 | https://en.wikipedia.org/w/index.php?title=277 | 277
prevalent method in Europe for naming years.
# Events.
onlyinclude
## By place.
### Roman Empire.
- Emperor Probus travels with his army west across the Sea of Marmara (Turkey) and through the provinces of Thrace, Moesia, and Pannonia to defeat the Goths along the lower Danube. He acquires from the troops the ... | 31,539 |
43749 | 278 | https://en.wikipedia.org/w/index.php?title=278 | 278
278
Year 278 (CCLXXVIII) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Probus and Lupus (or, less frequently, year 1031 "Ab urbe condita"). The denomination 278 for this year has been used since the ear... | 31,540 |
43749 | 278 | https://en.wikipedia.org/w/index.php?title=278 | 278
He expels the Franks from Gaul and reorganizes the Roman defenses on the Rhine.
- Probus resettles the Germanic tribes in the devastated provinces of the Roman Empire. He adopts the titles of "Gothicus Maximus" and "Germanicus Maximus".
- Piracy along the coast of Lycia and Pamphylia: The Romans besiege the city ... | 31,541 |
43753 | 276 | https://en.wikipedia.org/w/index.php?title=276 | 276
276
Year 276 (CCLXXVI) was a leap year starting on Saturday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Tacitus and Aemilianus (or, less frequently, year 1029 "Ab urbe condita"). The denomination 276 for this year has been used since the ... | 31,542 |
43753 | 276 | https://en.wikipedia.org/w/index.php?title=276 | 276
Tacitus dies of illness or is murdered at Tyana in Cappadocia.
- Florianus becomes Roman Emperor; he breaks off his campaign against the Heruli and marches from the Bosporus with support from the Roman legions in Britain, Gaul, Spain and Italy to fight an indecisive battle with Marcus Aurelius Probus in Cilicia.
... | 31,543 |
43753 | 276 | https://en.wikipedia.org/w/index.php?title=276 | 276
in which the Zoroastrian priests at Ctesiphon (Iran) put pressure on him to persecute Buddhists, Christians, and Manichaeans. He is succeeded by his son Bahram II.
### Sri Lanka.
- Reign of Mahasena in Ceylon. Orthodox and unpopular, he tries to introduce Mahayana Buddhism to the country.
/onlyinclude
# Births.... | 31,544 |
43754 | 275 | https://en.wikipedia.org/w/index.php?title=275 | 275
275
Year 275 (CCLXXV) was a common year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Aurelianus and Marcellinus (or, less frequently, year 1028 "Ab urbe condita"). The denomination 275 for this year has been used since t... | 31,545 |
43754 | 275 | https://en.wikipedia.org/w/index.php?title=275 | 275
high-ranking officers marked for execution.
- September – Aurelian falls victim to a conspiracy of the Praetorian Guard and is murdered near Byzantium (Turkey).
- September 25 – Marcus Claudius Tacitus is proclaimed Emperor by the Senate, his half brother Marcus Annius Florianus becomes Praetorian prefect.
- Gau... | 31,546 |
43754 | 275 | https://en.wikipedia.org/w/index.php?title=275 | 275
tim to a conspiracy of the Praetorian Guard and is murdered near Byzantium (Turkey).
- September 25 – Marcus Claudius Tacitus is proclaimed Emperor by the Senate, his half brother Marcus Annius Florianus becomes Praetorian prefect.
- Gaul is pillaged by the Franks and the Alemanni.
### India.
- The Pallava dyna... | 31,547 |
43755 | 250 | https://en.wikipedia.org/w/index.php?title=250 | 250
250
Year 250 (CCL) was a common year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Traianus and Gratus (or, less frequently, year 1003 "Ab urbe condita"). The denomination 250 for this year has been used since the early ... | 31,548 |
43755 | 250 | https://en.wikipedia.org/w/index.php?title=250 | 250
Romans lose the battle against the Goths
- Cniva lays siege to Philippopolis (modern Plovdiv). After a long resistance, Cniva conquers the city and slays its one hundred thousand inhabitants.
- The Alamanni drive the Romans from the modern area of Donau-Ries.
- An epidemic begins in Ethiopia, moves into Egypt an... | 31,549 |
43755 | 250 | https://en.wikipedia.org/w/index.php?title=250 | 250
rebuilt as a four-quartered cosmogram by Zapotec architects brought from Monte Albán in Oaxaca.
- Classic period of Mesoamerican civilization begins.
## By topic.
### Arts and sciences.
- Diophantus writes "Arithmetica", the first systematic treatise on algebra.
- Family Group, traditionally called the Family ... | 31,550 |
43755 | 250 | https://en.wikipedia.org/w/index.php?title=250 | 250
Emperor Decius institutes the persecution of Christians in an attempt to restore the religion of Rome. Pope Fabian is one of the first martyrs.
- Saint Denis, who is a patron saint of France, is beheaded around this time.
/onlyinclude
# Births.
- March 31 – Constantius Chlorus, Roman Emperor (d. 306)
- Gaius G... | 31,551 |
43755 | 250 | https://en.wikipedia.org/w/index.php?title=250 | 250
estore the religion of Rome. Pope Fabian is one of the first martyrs.
- Saint Denis, who is a patron saint of France, is beheaded around this time.
/onlyinclude
# Births.
- March 31 – Constantius Chlorus, Roman Emperor (d. 306)
- Gaius Galerius Valerius Maximianus, Roman Emperor (d. 311)
- Maximian, Roman Emp... | 31,552 |
43756 | 252 | https://en.wikipedia.org/w/index.php?title=252 | 252
252
Year 252 (CCLII) was a leap year starting on Thursday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Trebonianus and Volusianus (or, less frequently, year 1005 "Ab urbe condita"). The denomination 252 for this year has been used since th... | 31,553 |
43756 | 252 | https://en.wikipedia.org/w/index.php?title=252 | 252
men strong, yet this is unlikely.
### Persia.
- Shapur I, king of Persia, puts the revolt in Khorasan (Iran and Turkmenistan) down and rejoins with his army.
- He invades Armenia and appoints Artavazd VI as the new Armenian king.
- Georgia submits peacefully to Shapur I, and is made a special province in the Pe... | 31,554 |
43756 | 252 | https://en.wikipedia.org/w/index.php?title=252 | 252
- He invades Armenia and appoints Artavazd VI as the new Armenian king.
- Georgia submits peacefully to Shapur I, and is made a special province in the Persian Empire.
### China.
- Sun Liang succeeds his father Sun Quan as emperor of the Chinese state of Eastern Wu.
## By topic.
### Religion.
- Pope Cornelius... | 31,555 |
43757 | 256 | https://en.wikipedia.org/w/index.php?title=256 | 256
256
Year 256 (CCLVI) was a leap year starting on Tuesday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Claudius and Glabrio (or, less frequently, year 1009 "Ab urbe condita"). The denomination 256 for this year has been used since the early... | 31,556 |
43757 | 256 | https://en.wikipedia.org/w/index.php?title=256 | 256
cross the Rhine; the Alemanni reach Mediolanum (Milan). (disputed date)
- In Africa, the Berbers massacre Roman colonists.
- King Shapur I of the Sasanian Empire invades Mesopotamia and Syria. He conquers and plunders Antioch, destroys Dura-Europos and sacks the Anatolian city of Zeugma on the Euphrates. A devast... | 31,557 |
43757 | 256 | https://en.wikipedia.org/w/index.php?title=256 | 256
the kingdom is ruled by ministers on their behalf.
## By topic.
### Medicine.
- The great pandemic of the Roman world strikes violently in Pontus on the Black Sea and causes enormous loss of life in Alexandria, encouraging thousands to embrace Christianity.
### Religion.
- Emperor Valerian persecutes Christian... | 31,558 |
43757 | 256 | https://en.wikipedia.org/w/index.php?title=256 | 256
nicate Cyprian, bishop of Carthage, and other bishops in Africa and Asia Minor unless they stop rebaptizing heretics. Cyprian attacks the Pope in a treatise that gains support from the Council of Carthage. He sends envoys to Rome, raising the specter of a schism between the Roman and Carthaginian Churches.
- A Syn... | 31,559 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
Linear programming
Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical program... | 31,560 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
is a real-valued affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polyhedron where this function has the smallest (or largest) value if such a point exists.
Linear programs are problems that can be expressed in canonical form as
where x repres... | 31,561 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
optimized. In this context, two vectors are comparable when they have the same dimensions. If every entry in the first is less-than or equal-to the corresponding entry in the second, then it can be said that the first vector is less-than or equal-to the second vector.
Linear programming can be appli... | 31,562 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
of solving a system of linear inequalities dates back at least as far as Fourier, who in 1827 published a method for solving them, and after whom the method of Fourier–Motzkin elimination is named.
In 1939 a linear programming formulation of a problem that is equivalent to the general linear program... | 31,563 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
Koopmans formulated classical economic problems as linear programs. Kantorovich and Koopmans later shared the 1975 Nobel prize in economics. In 1941, Frank Lauren Hitchcock also formulated transportation problems as linear programs and gave a solution very similar to the later simplex method. Hitchco... | 31,564 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
Neumann to discuss his simplex method, Neumann immediately conjectured the theory of duality by realizing that the problem he had been working in game theory was equivalent. Dantzig provided formal proof in an unpublished report "A Theorem on Linear Inequalities" on January 5, 1948. In the post-war y... | 31,565 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
by posing the problem as a linear program and applying the simplex algorithm. The theory behind linear programming drastically reduces the number of possible solutions that must be checked.
The linear programming problem was first shown to be solvable in polynomial time by Leonid Khachiyan in 1979, ... | 31,566 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
programming, such as "network flow" problems and "multicommodity flow" problems are considered important enough to have generated much research on specialized algorithms for their solution. A number of algorithms for other types of optimization problems work by solving LP problems as sub-problems. Hi... | 31,567 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
and other issues. Although the modern management issues are ever-changing, most companies would like to maximize profits and minimize costs with limited resources. Therefore, many issues can be characterized as linear programming problems.
# Standard form.
"Standard form" is the usual and most intu... | 31,568 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
variables can always be rewritten into an equivalent problem in standard form.
## Example.
Suppose that a farmer has a piece of farm land, say "L" km, to be planted with either wheat or barley or some combination of the two. The farmer has a limited amount of fertilizer, "F" kilograms, and pesticid... | 31,569 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
then profit can be maximized by choosing optimal values for "x" and "x". This problem can be expressed with the following linear programming problem in the standard form:
In matrix form this becomes:
# Augmented form (slack form).
Linear programming problems can be converted into an "augmented for... | 31,570 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
example above is converted into the following augmented form:
where formula_15 are (non-negative) slack variables, representing in this example the unused area, the amount of unused fertilizer, and the amount of unused pesticide.
In matrix form this becomes:
# Duality.
Every linear programming pr... | 31,571 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
linear program. Additionally, every feasible solution for a linear program gives a bound on the optimal value of the objective function of its dual. The weak duality theorem states that the objective function value of the dual at any feasible solution is always greater than or equal to the objective ... | 31,572 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
the primal must be infeasible. However, it is possible for both the dual and the primal to be infeasible. See dual linear program for details and several more examples.
# Variations.
## Covering/packing dualities.
A covering LP is a linear program of the form:
such that the matrix "A" and the vec... | 31,573 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
problem, the independent set problem, and the matching problem are packing LPs. The LP relaxations of the set cover problem, the vertex cover problem, and the dominating set problem are also covering LPs.
Finding a fractional coloring of a graph is another example of a covering LP. In this case, the... | 31,574 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
Let (w, w, ..., w) denote the corresponding primal slack variables, and let (z, z, ... , z) denote the corresponding dual slack variables. Then x and y are optimal for their respective problems if and only if
- x z = 0, for "j" = 1, 2, ... , "n", and
- w y = 0, for "i" = 1, 2, ... , "m".
So if the... | 31,575 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
there are "leftovers"), then additional quantities of that resource must have no value. Likewise, if there is slack in the dual (shadow) price non-negativity constraint requirement, i.e., the price is not zero, then there must be scarce supplies (no "leftovers").
# Theory.
## Existence of optimal s... | 31,576 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
are inconsistent, then no feasible solution exists: For instance, the constraints x ≥ 2 and x ≤ 1 cannot be satisfied jointly; in this case, we say that the LP is "infeasible". Second, when the polytope is unbounded in the direction of the gradient of the objective function (where the gradient of the... | 31,577 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
constraint set, by the "maximum principle" for "convex functions" (alternatively, by the "minimum" principle for "concave functions") since linear functions are both convex and concave. However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to ... | 31,578 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
called "basic feasible solutions". The reason for this choice of name is as follows. Let "d" denote the number of variables. Then the fundamental theorem of linear inequalities implies (for feasible problems) that for every vertex x of the LP feasible region, there exists a set of "d" (or fewer) ineq... | 31,579 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
Simplex algorithm of Dantzig.
The simplex algorithm, developed by George Dantzig in 1947, solves LP problems by constructing a feasible solution at a vertex of the polytope and then walking along a path on the edges of the polytope to vertices with non-decreasing values of the objective function unt... | 31,580 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
certain precautions against "cycling" are taken. The simplex algorithm has been proved to solve "random" problems efficiently, i.e. in a cubic number of steps, which is similar to its behavior on practical problems.
However, the simplex algorithm has poor worst-case behavior: Klee and Minty construc... | 31,581 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
pivots between bases. However, the criss-cross algorithm need not maintain feasibility, but can pivot rather from a feasible basis to an infeasible basis. The criss-cross algorithm does not have polynomial time-complexity for linear programming. Both algorithms visit all 2 corners of a (perturbed) cu... | 31,582 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
for linear programming. To solve a problem which has "n" variables and can be encoded in "L" input bits, this algorithm uses "O(nL)" pseudo-arithmetic operations on numbers with "O(L)" digits. Leonid Khachiyan solved this long-standing complexity issue in 1979 with the introduction of the ellipsoid m... | 31,583 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
as the simplex method is more efficient for all but specially constructed families of linear programs.
However, Khachiyan's algorithm inspired new lines of research in linear programming. In 1984, N. Karmarkar proposed a projective method for linear programming. Karmarkar's algorithm improved on Kha... | 31,584 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
It was developed in the Soviet Union in the mid-1960s, but didn't receive much attention until the discovery of Karmarkar's algorithm, after which affine scaling was reinvented multiple times and presented as a simplified version of Karmarkar's. Affine scaling amounts to doing gradient descent steps ... | 31,585 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
the number of bits.
### Path-following algorithms.
For both theoretical and practical purposes, barrier function or path-following methods have been the most popular interior point methods since the 1990s. In 2015, Lee and Sidford showed that, it can be solved in formula_24 time, and it remains tak... | 31,586 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
However, for specific types of LP problems, it may be that one type of solver is better than another (sometimes much better), and that the structure of the solutions generated by interior point methods versus simplex-based methods are significantly different with the support set of active variables b... | 31,587 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
in time , and the best known parallel algorithm of this kind runs in iterations, each requiring only a matrix-vector multiplication which is highly parallelizable.
# Open problems and recent work.
There are several open problems in the theory of linear programming, the solution of which would repre... | 31,588 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
set of problems has been cited by Stephen Smale as among the 18 greatest unsolved problems of the 21st century. In Smale's words, the third version of the problem "is the main unsolved problem of linear programming theory." While algorithms exist to solve linear programming in weakly polynomial time,... | 31,589 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
higher dimensions, it still leaves the following questions open.
- Are there pivot rules which lead to polynomial-time simplex variants?
- Do all polytopal graphs have polynomially bounded diameter?
These questions relate to the performance analysis and development of simplex-like methods. The imm... | 31,590 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
simplex algorithm and its variants fall in the family of edge-following algorithms, so named because they solve linear programming problems by moving from vertex to vertex along edges of a polytope. This means that their theoretical performance is limited by the maximum number of edges between any tw... | 31,591 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
time. Questions about polytope diameter are of independent mathematical interest.
Simplex pivot methods preserve primal (or dual) feasibility. On the other hand, criss-cross pivot methods do not preserve (primal or dual) feasibility—they may visit primal feasible, dual feasible or primal-and-dual in... | 31,592 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
without resolving questions about the diameter of general polytopes.
# Integer unknowns.
If all of the unknown variables are required to be integers, then the problem is called an integer programming (IP) or integer linear programming (ILP) problem. In contrast to linear programming, which can be s... | 31,593 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
one of Karp's 21 NP-complete problems.
If only some of the unknown variables are required to be integers, then the problem is called a mixed integer programming (MIP) problem. These are generally also NP-hard because they are even more general than ILP programs.
There are however some important sub... | 31,594 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
cut
- Branch and price
- if the problem has some extra structure, it may be possible to apply delayed column generation.
Such integer-programming algorithms are discussed by Padberg and in Beasley.
# Integral linear programs.
A linear program in real variables is said to be integral if it has at... | 31,595 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
"c", the optimal "value" of the linear program formula_29 is an integer.
Integral linear programs are of central importance in the polyhedral aspect of combinatorial optimization since they provide an alternate characterization of a problem. Specifically, for any problem, the convex hull of the solu... | 31,596 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
so one should be careful to distinguish the following two concepts,
- in an "integer linear program," described in the previous section, variables are forcibly constrained to be integers, and this problem is NP-hard in general,
- in an "integral linear program," described in this section, variables... | 31,597 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
general methods including the integer decomposition property and total dual integrality. Other specific well-known integral LPs include the matching polytope, lattice polyhedra, submodular flow polyhedra, and the intersection of 2 generalized polymatroids/"g"-polymatroids – e.g. see Schrijver 2003.
... | 31,598 |
43730 | Linear programming | https://en.wikipedia.org/w/index.php?title=Linear%20programming | Linear programming
See also.
- Convex programming
- Dynamic programming
- Input–output model
- Job shop scheduling
- Linear-fractional programming (LFP)
- LP-type problem
- Mathematical programming
- Nonlinear programming
- Oriented matroid
- Quadratic programming, a superset of linear programming
- Semidefi... | 31,599 |
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