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In logic, a functionally complete set of logical connectives or Boolean operators is one that can be used to express all possible truth tables by combining members of the set into a Boolean expression. A well-known complete set of connectives is { AND, NOT }. Each of the singleton sets { NAND } and { NOR } is functiona... | Wikipedia/Functional_completeness |
In propositional logic, tautology is either of two commonly used rules of replacement. The rules are used to eliminate redundancy in disjunctions and conjunctions when they occur in logical proofs. They are:
The principle of idempotency of disjunction:
P
∨
P
⇔
P
... | Wikipedia/Tautology_(rule_of_inference) |
Chaff is an algorithm for solving instances of the Boolean satisfiability problem in programming. It was designed by researchers at Princeton University. The algorithm is an instance of the DPLL algorithm with a number of enhancements for efficient implementation.
== Implementations ==
Some available implementations ... | Wikipedia/Chaff_algorithm |
"Function and Concept" (German: "Funktion und Begriff", "Function and Concept") is a lecture delivered by Gottlob Frege in 1891. The lecture involves a clarification of his earlier distinction between concepts and objects. It was first published as an article in 1962.
== Overview ==
In general, a concept is a functio... | Wikipedia/Function_and_Concept |
A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that... | Wikipedia/False_dilemma |
An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914. They include both a separate graphical notation for logical statements and a logical c... | Wikipedia/Entitative_graph |
An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914. They include both a separate graphical notation for logical statements and a logical c... | Wikipedia/Logical_graph |
The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (e.g., general prevalence) in favor of the individuating information (i.e., information pertaining only to a specific case). For example, if someone hears that a friend is very shy a... | Wikipedia/Base_rate_fallacy |
In mathematical logic, the implicational propositional calculus is a version of classical propositional calculus that uses only one connective, called implication or conditional. In formulas, this binary operation is indicated by "implies", "if ..., then ...", "→", "
→
{\displayst... | Wikipedia/Implicational_propositional_calculus |
Constructive dilemma is a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either P or R is true, then either Q or S has to be true. In sum, if two conditionals are true and at least one of their antecedents is, then at least one of their consequents must be t... | Wikipedia/Constructive_dilemma |
An existential graph is a type of diagrammatic or visual notation for logical expressions, created by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914. They include both a separate graphical notation for logical statements and a logical c... | Wikipedia/Existential_graph |
Rules of inference are ways of deriving conclusions from premises. They are integral parts of formal logic, serving as norms of the logical structure of valid arguments. If an argument with true premises follows a rule of inference then the conclusion cannot be false. Modus ponens, an influential rule of inference, con... | Wikipedia/Inference_rule |
A propositional directed acyclic graph (PDAG) is a data structure that is used to represent a Boolean function. A Boolean function can be represented as a rooted, directed acyclic graph of the following form:
Leaves are labeled with
⊤
{\displaystyle \top }
(true),
... | Wikipedia/Propositional_directed_acyclic_graph |
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation-complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsa... | Wikipedia/Resolution_(logic) |
In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios a deductive system is first understood from context, giving rise to a formal system that combines the language with deduction rules. An element
ϕ
∈
T
... | Wikipedia/First-order_theory |
Cirquent calculus is a proof calculus that manipulates graph-style constructs termed cirquents, as opposed to the traditional tree-style objects such as formulas or sequents. Cirquents come in a variety of forms, but they all share one main characteristic feature, making them different from the more traditional objects... | Wikipedia/Cirquent_calculus |
A metatheory or meta-theory is a theory on a subject matter that is a theory in itself. Analyses or descriptions of an existing theory would be considered meta-theories. For mathematics and mathematical logic, a metatheory is a mathematical theory about another mathematical theory. Meta-theoretical investigations are p... | Wikipedia/Metatheory |
In geometry, Cavalieri's principle, a modern implementation of the method of indivisibles, named after Bonaventura Cavalieri, is as follows:
2-dimensional case: Suppose two regions in a plane are included between two parallel lines in that plane. If every line parallel to these two lines intersects both regions in lin... | Wikipedia/Method_of_indivisibles |
The Book of Lemmas or Book of Assumptions (Arabic Maʾkhūdhāt Mansūba ilā Arshimīdis) is a book attributed to Archimedes by Thābit ibn Qurra, though the authorship of the book is questionable. It consists of fifteen propositions (lemmas) on circles.
== History ==
=== Translations ===
The Book of Lemmas was first int... | Wikipedia/Book_of_Lemmas |
In mathematics, and specifically in measure theory, equivalence is a notion of two measures being qualitatively similar. Specifically, the two measures agree on which events have measure zero.
== Definition ==
Let
μ
{\displaystyle \mu }
and
ν
... | Wikipedia/Equivalence_(measure_theory) |
In mathematics, nonstandard calculus is the modern application of infinitesimals, in the sense of nonstandard analysis, to infinitesimal calculus. It provides a rigorous justification for some arguments in calculus that were previously considered merely heuristic.
Non-rigorous calculations with infinitesimals were wide... | Wikipedia/Non-standard_calculus |
Fads and Fallacies in the Name of Science (1957)—originally published in 1952 as In the Name of Science: An Entertaining Survey of the High Priests and Cultists of Science, Past and Present—was Martin Gardner's second book. A survey of what it described as pseudosciences and cult beliefs, it became a founding document ... | Wikipedia/Fads_and_Fallacies_in_the_Name_of_Science |
Science Fiction Puzzle Tales is a book written by Martin Gardner. It is a book of puzzles and short stories that relate to them.
== Reception ==
Dave Langford reviewed Science Fiction Puzzle Tales for White Dwarf #47, and stated that "Many are familiar from Gardner's former books, but he's added new twists to fool sm... | Wikipedia/Science_Fiction_Puzzle_Tales |
The crocodile paradox, also known as crocodile sophism, is a paradox in logic in the same family of paradoxes as the liar paradox. The premise states that a crocodile, who has stolen a child, promises the parent that their child will be returned if and only if they correctly predict what the crocodile will do next.
The... | Wikipedia/Crocodile_dilemma |
Monetary circuit theory is a heterodox theory of monetary economics, particularly money creation, often associated with the post-Keynesian school.
It holds that money is created endogenously by the banking sector, rather than exogenously by central bank lending; it is a theory of endogenous money. It is also called cir... | Wikipedia/Monetary_circuit_theory |
Decision field theory (DFT) is a dynamic-cognitive approach to human decision making. It is a cognitive model that describes how people actually make decisions rather than a rational or normative theory that prescribes what people should or ought to do. It is also a dynamic model of decision-making rather than a static... | Wikipedia/Decision_field_theory |
Emotional choice theory (also referred to as the "logic of affect") is a social scientific action model to explain human decision-making. Its foundation was laid in Robin Markwica’s monograph Emotional Choices published by Oxford University Press in 2018. It is associated with its own method for identifying emotions an... | Wikipedia/Emotional_choice_theory |
Behavioural science is the branch of science concerned with human behaviour. While the term can technically be applied to the study of behaviour amongst all living organisms, it is nearly always used with reference to humans as the primary target of investigation (though animals may be studied in some instances, e.g. i... | Wikipedia/Behavioural_sciences |
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings.
In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function. This kind of utility bears a closer... | Wikipedia/Utility_theory |
The hedgehog's dilemma, or sometimes the porcupine dilemma, is a metaphor about the challenges of human intimacy. It describes a situation in which a group of hedgehogs seek to move close to one another to share heat during cold weather. They must remain apart, however, as they cannot avoid hurting one another with the... | Wikipedia/Hedgehog's_dilemma |
Mutualism is an anarchist school of thought and economic theory that advocates for workers' control of the means of production, a free market made up of individual artisans, sole proprietorships and workers' cooperatives, and occupation and use property rights. As proponents of the labour theory of value and labour the... | Wikipedia/Mutualism_(economic_theory) |
In decision theory, Savage's subjective expected utility model (also known as Savage's framework, Savage's axioms, or Savage's representation theorem) is a formalization of subjective expected utility (SEU) developed by Leonard J. Savage in his 1954 book The Foundations of Statistics, based on previous work by Ramsey,... | Wikipedia/Savage's_subjective_expected_utility_model |
Causal decision theory (CDT) is a school of thought within decision theory which states that, when a rational agent is confronted with a set of possible actions, one should select the action which causes the best outcome in expectation. CDT contrasts with evidential decision theory (EDT), which recommends the action wh... | Wikipedia/Causal_decision_theory |
Victor Vroom, a professor at Yale University and a scholar on leadership and decision-making, developed the normative model of decision-making. Drawing upon literature from the areas of leadership, group decision-making, and procedural fairness, Vroom’s model predicts the effectiveness of decision-making procedures. Sp... | Wikipedia/Normative_model_of_decision-making |
The exploration–exploitation dilemma, also known as the explore–exploit tradeoff, is a fundamental concept in decision-making that arises in many domains. It is depicted as the balancing act between two opposing strategies. Exploitation involves choosing the best option based on current knowledge of the system (which m... | Wikipedia/Exploration–exploitation_dilemma |
Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. It uses measures of possibility and necessity between 0 and 1, ranging from impossible to possible and unnecessary to necessary, respectively. Professor Lotfi Zadeh first introduced pos... | Wikipedia/Possibility_theory |
In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating... | Wikipedia/Bayesian_decision_theory |
The decision-matrix method, also Pugh method or Pugh concept selection, invented by Stuart Pugh, is a qualitative technique used to rank the multi-dimensional options of an option set. It is frequently used in engineering for making design decisions but can also be used to rank investment options, vendor options, produ... | Wikipedia/Decision-matrix_method |
Prospect theory is a theory of behavioral economics, judgment and decision making that was developed by Daniel Kahneman and Amos Tversky in 1979. The theory was cited in the decision to award Kahneman the 2002 Nobel Memorial Prize in Economics.
Based on results from controlled studies, it describes how individuals asse... | Wikipedia/Prospect_theory |
The analytic network process (ANP) is a more general form of the analytic hierarchy process (AHP) used in multi-criteria decision analysis.
AHP structures a decision problem into a hierarchy with a goal, decision criteria, and alternatives, while the ANP structures it as a network. Both then use a system of pairwise co... | Wikipedia/Analytic_network_process |
Fuzzy-trace theory (FTT) is a theory of cognition originally proposed by Valerie F. Reyna and Charles Brainerd to explain cognitive phenomena, particularly in memory and reasoning.
FTT posits two types of memory processes (verbatim and gist) and, therefore, it is often referred to as a dual process theory of memory. Ac... | Wikipedia/Fuzzy-trace_theory |
Choice modelling attempts to model the decision process of an individual or segment via revealed preferences or stated preferences made in a particular context or contexts. Typically, it attempts to use discrete choices (A over B; B over A, B & C) in order to infer positions of the items (A, B and C) on some relevant l... | Wikipedia/Choice_modelling |
In psychological theories of motivation, the Rubicon model, more completely the Rubicon model of action phases, makes a distinction between motivational and volitional processes. The Rubicon model "defines clear boundaries between motivational and action phases." The first boundary "separates the motivational process o... | Wikipedia/Rubicon_model |
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost" associated with the event. An optimization problem seeks to minimize a ... | Wikipedia/Risk_function |
In decision theory, the Anscombe-Aumann subjective expected utility model (also known as Anscombe-Aumann framework, Anscombe-Aumann approach, or Anscombe-Aumann representation theorem) is a framework to formalizing subjective expected utility (SEU) developed by Frank Anscombe and Robert Aumann.
Anscombe and Aumann's ap... | Wikipedia/Anscombe-Aumann_subjective_expected_utility_model |
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings.
In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function. This kind of utility bears a closer... | Wikipedia/Utility_function |
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, the compounding frequency, and the length of time over which it is lent, dep... | Wikipedia/Interest_rate |
In decision theory, regret aversion (or anticipated regret) describes how the human emotional response of regret can influence decision-making under uncertainty. When individuals make choices without complete information, they often experience regret if they later discover that a different choice would have produced a ... | Wikipedia/Regret_(decision_theory) |
Info-gap decision theory seeks to optimize robustness to failure under severe uncertainty, in particular applying sensitivity analysis of the stability radius type to perturbations in the value of a given estimate of the parameter of interest. It has some connections with Wald's maximin model; some authors distinguish ... | Wikipedia/Info-gap_decision_theory |
Real business-cycle theory (RBC theory) is a class of new classical macroeconomics models in which business-cycle fluctuations are accounted for by real, in contrast to nominal, shocks. RBC theory sees business cycle fluctuations as the efficient response to exogenous changes in the real economic environment. That is, ... | Wikipedia/Real_business-cycle_theory |
Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions regarding the allocation of scarce resources and the interactions among these individuals and firms. Microeconomics focuses on the study of individual markets, sectors, or industries as opposed to the economy ... | Wikipedia/Price_theory |
Evidential decision theory (EDT) is a school of thought within decision theory which states that, when a rational agent is confronted with a set of possible actions, one should select the action with the highest news value, that is, the action which would be indicative of the best outcome in expectation if one received... | Wikipedia/Evidential_decision_theory |
Modern monetary theory or modern money theory (MMT) is a heterodox macroeconomic theory that describes currency as a public monopoly and unemployment as evidence that a currency monopolist is overly restricting the supply of the financial assets needed to pay taxes and satisfy savings desires. According to MMT, governm... | Wikipedia/Modern_monetary_theory |
Rational choice modeling refers to the use of decision theory (the theory of rational choice) as a set of guidelines to help understand economic and social behavior. The theory tries to approximate, predict, or mathematically model human behavior by analyzing the behavior of a rational actor facing the same costs and b... | Wikipedia/Rational_choice_models |
The theory of belief functions, also referred to as evidence theory or Dempster–Shafer theory (DST), is a general framework for reasoning with uncertainty, with understood connections to other frameworks such as probability, possibility and imprecise probability theories. First introduced by Arthur P. Dempster in the ... | Wikipedia/Dempster–Shafer_theory |
In mechanics, the net force is the sum of all the forces acting on an object. For example, if two forces are acting upon an object in opposite directions, and one force is greater than the other, the forces can be replaced with a single force that is the difference of the greater and smaller force. That force is the ne... | Wikipedia/Net_force |
In physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which a... | Wikipedia/Polygon_of_forces |
In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original ... | Wikipedia/Resultant_force |
Borůvka's algorithm is a greedy algorithm for finding a minimum spanning tree in a graph,
or a minimum spanning forest in the case of a graph that is not connected.
It was first published in 1926 by Otakar Borůvka as a method of constructing an efficient electricity network for Moravia.
The algorithm was rediscovered b... | Wikipedia/Borůvka's_algorithm |
Dijkstra's algorithm ( DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example, a road network. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.
Dijkstra's algorithm finds the shortest path from a gi... | Wikipedia/Dijkstra's_algorithm |
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM be... | Wikipedia/Response_surface_methodology |
Powell's dog leg method, also called Powell's hybrid method, is an iterative optimisation algorithm for the solution of non-linear least squares problems, introduced in 1970 by Michael J. D. Powell. Similarly to the Levenberg–Marquardt algorithm, it combines the Gauss–Newton algorithm with gradient descent, but it uses... | Wikipedia/Powell's_dog_leg_method |
In numerical analysis, a quasi-Newton method is an iterative numerical method used either to find zeroes or to find local maxima and minima of functions via an iterative recurrence formula much like the one for Newton's method, except using approximations of the derivatives of the functions in place of exact derivative... | Wikipedia/Quasi-Newton_method |
In constrained optimization, a field of mathematics, a barrier function is a continuous function whose value increases to infinity as its argument approaches the boundary of the feasible region of an optimization problem. Such functions are used to replace inequality constraints by a penalizing term in the objective f... | Wikipedia/Barrier_function |
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice.
Denoting by
... | Wikipedia/Karmarkar's_algorithm |
In the design of experiments, optimal experimental designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith.
In the design of experiments for estimating s... | Wikipedia/Optimal_design |
In mathematics, the spiral optimization (SPO) algorithm is a metaheuristic inspired by spiral phenomena in nature.
The first SPO algorithm was proposed for two-dimensional unconstrained optimization
based on two-dimensional spiral models. This was extended to n-dimensional problems by generalizing the two-dimensional s... | Wikipedia/Spiral_optimization_algorithm |
In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so... | Wikipedia/BFGS_method |
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NP-hard problems) with provable guarantees on the distance of the returned solution to the optimal one. Approximation algorithms naturally arise in the f... | Wikipedia/Approximation_algorithm |
A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locally optimal solutions that approximate a globally optimal solution in a reason... | Wikipedia/Greedy_algorithm |
The Nelder–Mead method (also downhill simplex method, amoeba method, or polytope method) is a numerical method used to find the minimum or maximum of an objective function in a multidimensional space. It is a direct search method (based on function comparison) and is often applied to nonlinear optimization problems for... | Wikipedia/Nelder–Mead_method |
Powell's method, strictly Powell's conjugate direction method, is an algorithm proposed by Michael J. D. Powell for finding a local minimum of a function. The function need not be differentiable, and no derivatives are taken.
The function must be a real-valued function of a fixed number of real-valued inputs. The calle... | Wikipedia/Powell's_method |
Augmented Lagrangian methods are a certain class of algorithms for solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series of unconstrained problems and add a penalty term to the objective, but the augmented Lagrangian met... | Wikipedia/Augmented_Lagrangian_method |
Subgradient methods are convex optimization methods which use subderivatives. Originally developed by Naum Z. Shor and others in the 1960s and 1970s, subgradient methods are convergent when applied even to a non-differentiable objective function. When the objective function is differentiable, sub-gradient methods for u... | Wikipedia/Subgradient_method |
Dinic's algorithm or Dinitz's algorithm is a strongly polynomial algorithm for computing the maximum flow in a flow network, conceived in 1970 by Israeli (formerly Soviet) computer scientist Yefim Dinitz. The algorithm runs in
O
(
|
V
... | Wikipedia/Dinic's_algorithm |
In computer science, Prim's algorithm is a greedy algorithm that finds a minimum spanning tree for a weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. The algorithm operates by building thi... | Wikipedia/Prim's_algorithm |
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numb... | Wikipedia/Bellman–Ford_algorithm |
Bayesian experimental design provides a general probability-theoretical framework from which other theories on experimental design can be derived. It is based on Bayesian inference to interpret the observations/data acquired during the experiment. This allows accounting for both any prior knowledge on the parameters to... | Wikipedia/Bayesian_experimental_design |
In mathematical optimization, the criss-cross algorithm is any of a family of algorithms for linear programming. Variants of the criss-cross algorithm also solve more general problems with linear inequality constraints and nonlinear objective functions; there are criss-cross algorithms for linear-fractional programming... | Wikipedia/Criss-cross_algorithm |
The design of experiments (DOE), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introdu... | Wikipedia/Design_of_experiments |
The Ford–Fulkerson method or Ford–Fulkerson algorithm (FFA) is a greedy algorithm that computes the maximum flow in a flow network. It is sometimes called a "method" instead of an "algorithm" as the approach to finding augmenting paths in a residual graph is not fully specified or it is specified in several implementat... | Wikipedia/Ford–Fulkerson_algorithm |
In mathematical optimization, penalty methods are a certain class of algorithms for solving constrained optimization problems.
A penalty method replaces a constrained optimization problem by a series of unconstrained problems whose solutions ideally converge to the solution of the original constrained problem. The un... | Wikipedia/Penalty_method |
In mathematical optimization, the push–relabel algorithm (alternatively, preflow–push algorithm) is an algorithm for computing maximum flows in a flow network. The name "push–relabel" comes from the two basic operations used in the algorithm. Throughout its execution, the algorithm maintains a "preflow" and gradually c... | Wikipedia/Push–relabel_maximum_flow_algorithm |
In computer science, the Edmonds–Karp algorithm is an implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network in
O
(
|
V
|
|
E
... | Wikipedia/Edmonds–Karp_algorithm |
In computer science, the Floyd–Warshall algorithm (also known as Floyd's algorithm, the Roy–Warshall algorithm, the Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding shortest paths in a directed weighted graph with positive or negative edge weights (but with no negative cycles). A single execution ... | Wikipedia/Floyd–Warshall_algorithm |
Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criteria, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise... | Wikipedia/Optimization_algorithm |
In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, ... | Wikipedia/Cutting-plane_method |
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-semidefinite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be hand... | Wikipedia/Conjugate_gradient_method |
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorit... | Wikipedia/Levenberg–Marquardt_algorithm |
In mathematical optimization, the active-set method is an algorithm used to identify the active constraints in a set of inequality constraints. The active constraints are then expressed as equality constraints, thereby transforming an inequality-constrained problem into a simpler equality-constrained subproblem.
An op... | Wikipedia/Active-set_method |
In mathematical optimization, Lemke's algorithm is a procedure for solving linear complementarity problems, and more generally mixed linear complementarity problems. It is named after Carlton E. Lemke.
Lemke's algorithm is of pivoting or basis-exchange type. Similar algorithms can compute Nash equilibria for two-person... | Wikipedia/Lemke's_algorithm |
The Frank–Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization. Also known as the conditional gradient method, reduced gradient algorithm and the convex combination algorithm, the method was originally proposed by Marguerite Frank and Philip Wolfe in 1956. In each itera... | Wikipedia/Frank–Wolfe_algorithm |
In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of ... | Wikipedia/Generalized_linear_model |
The general linear model or general multivariate regression model is a compact way of simultaneously writing several multiple linear regression models. In that sense it is not a separate statistical linear model. The various multiple linear regression models may be compactly written as
... | Wikipedia/General_linear_model |
In mathematical optimization, the revised simplex method is a variant of George Dantzig's simplex method for linear programming.
The revised simplex method is mathematically equivalent to the standard simplex method but differs in implementation. Instead of maintaining a tableau which explicitly represents the constrai... | Wikipedia/Revised_simplex_method |
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numb... | Wikipedia/Shortest_Path_Faster_Algorithm |
The Berndt–Hall–Hall–Hausman (BHHH) algorithm is a numerical optimization algorithm similar to the Newton–Raphson algorithm, but it replaces the observed negative Hessian matrix with the outer product of the gradient. This approximation is based on the information matrix equality and therefore only valid while maximizi... | Wikipedia/Berndt–Hall–Hall–Hausman_algorithm |
In mathematical optimization and computer science, heuristic (from Greek εὑρίσκω "I find, discover") is a technique designed for problem solving more quickly when classic methods are too slow for finding an exact or approximate solution, or when classic methods fail to find any exact solution in a search space. This i... | Wikipedia/Heuristic_algorithm |
Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree. It is a greedy algorithm that in each step adds to the forest the lowest-weight edge that will not form a cycle. The key steps of the algorithm are sorting and the use o... | Wikipedia/Kruskal's_algorithm |
In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems. Like the related Davidon–Fletcher–Powell method, BFGS determines the descent direction by preconditioning the gradient with curvature information. It does so... | Wikipedia/Broyden–Fletcher–Goldfarb–Shanno_algorithm |
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