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835c2398f7e8c8249c224d48e7cfa05006ad2d48 | abstract | 0 | 29 | Abstract | We propose a variant of the classical augmented Lagrangian method for
constrained optimization problems in Banach spaces. Our theoretical framework
does not require any convexity or second-order assumptions and allows the
treatment of inequality constraints with infinite-dimensional image space.
Moreover, we discuss th... | {
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} | 10.1137/16M1107103 | 1807.04467 | An Augmented Lagrangian Method for Optimization Problems in Banach
Spaces | [
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24f17002cb59f835a0ffe18e5c9a310152e57553 | subsection | 1 | 29 | Introduction | Let X, Y be (real) Banach spaces and let f:X\rightarrow \mathbb {R}, g:X\rightarrow Y be
given mappings. The aim of this paper is to describe an augmented Lagrangian
method for the solution of the constrained optimization problem\min \ f(x) \quad \text{subject to (s.t.)}\quad g(x)\le 0.We assume that Y\hookrightarrow L... | {
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... | 10.1137/16M1107103 | 1807.04467 | An Augmented Lagrangian Method for Optimization Problems in Banach
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"Christian Kanzow",
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c6774eeaa31db2b0bba9c7a4ebbb16cde32a113d | subsection | 2 | 29 | Introduction | The norms on X, Y, etc. are
denoted by \Vert \cdot \Vert , where an index (as in \Vert \cdot \Vert _X) is appended if necessary.
Furthermore, we write \rightarrow , \rightharpoonup , and \rightharpoonup ^* for strong, weak, and weak-^*
convergence, respectively. Finally, we use the abbreviation lsc for a lower
semicont... | {
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} | 10.1137/16M1107103 | 1807.04467 | An Augmented Lagrangian Method for Optimization Problems in Banach
Spaces | [
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9442428e98990dfcb9863210809d1c637a7cbad6 | subsection | 3 | 29 | Preliminaries and Assumptions | We denote by e:Y\rightarrow Z the (linear and continuous) dense embedding of Y into
Z:=L^2(\Omega ), and by K_Y, K_Z the respective nonnegative cones in
Y and Z, i.e.K_Z:=\lbrace z\in Z\mid z(t)\ge 0~\text{a.e.}\rbrace \quad \text{and}\quad K_Y:= \lbrace y\in Y \mid e(y) \in K_Z\rbrace .Note that the adjoint mapping e^... | {
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"raw": "C. Baiocchi and A. Capelo. Variational and Quasivariational Inequalities. John Wiley & Sons, Inc., New York, 1984.",
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f1ab019fe369649a5766d80f63daae0213b96fdc | subsection | 4 | 29 | Preliminaries and Assumptions | Hence, if \Vert g_+\Vert is convex (which is true if g is convex with respect to the order in Y), then
the (strong) lower semicontinuity of g already implies the weak lower
semicontinuity. We conclude that (A1) holds, in particular, for every
lsc. convex function f and any mapping g\in \mathcal {L}(X,Y).On a further no... | {
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60da3cf59d9c7494d114e3685aee14fef517830e | subsection | 5 | 29 | Preliminaries and Assumptions | For instance, consider the case where \Omega =\lbrace 1\rbrace and
Z=L^2(\Omega ), which can be identified with \mathbb {R}. Then the sequences
a^k=k and b^k=1/k provide a simple counterexample. | {
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} | 10.1137/16M1107103 | 1807.04467 | An Augmented Lagrangian Method for Optimization Problems in Banach
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eb0f67bdbb7a5023f11763a778802f595b66bc66 | subsection | 6 | 29 | An Augmented Lagrangian Method | This section gives a detailed statement of our augmented Lagrangian
method for the solution of the optimization problem (REF ).
It is motivated by the finite-dimensional discussion in, e.g.,
and differs from the traditional augmented
Lagrangian method as applied, e.g., in , to a class
of infinite-dimensional problems,... | {
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Spaces | [
"Christian Kanzow",
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047382410681af3ef9dc5009574dd699071d0e5c | subsection | 7 | 29 | An Augmented Lagrangian Method | "Going a\nlittle further, our method also includes the Moreau-Yosida regularization scheme\n(see , a(...TRUNCATED) | {"cite_spans":[{"arxiv_id":"","doi":"","end":185,"openalex_id":"","raw":"M. Hintermüller and K. Kun(...TRUNCATED) | 10.1137/16M1107103 | 1807.04467 | An Augmented Lagrangian Method for Optimization Problems in Banach
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7654f86924960682501f2cfe947ba575ad46a01c | subsection | 8 | 29 | Global Minimization | "We begin by considering Algorithm REF from a global optimization\nperspective. Note that most of th(...TRUNCATED) | {
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9cfbf62dd0ef0291621a5f640f345a0db0d9bc07 | subsection | 9 | 29 | Global Minimization | "Let \\mathcal {K}\\subset \\mathbb {N}\nbe such that x^{k+1}\\rightharpoonup _{\\mathcal {K}}\\bar{(...TRUNCATED) | {
"cite_spans": []
} | 10.1137/16M1107103 | 1807.04467 | An Augmented Lagrangian Method for Optimization Problems in Banach
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"Christian Kanzow",
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"math.OC"
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End of preview. Expand in Data Studio
EviGraph-R Dense Index
This dataset contains the dense retrieval index generated by the EviGraph-R indexing pipeline. It is exported from the finalized shard records after the collection has been written to Qdrant, so the Hub copy matches the indexed corpus that was prepared for retrieval.
What is inside
- One row per indexed chunk.
- Original chunk payload metadata used by retrieval and analysis.
- Vector columns:
dense_vector. - Source collection:
unarxive_chunks. - Embedding model key:
bge-m3. - Runtime profile:
hpc.
Build summary
- Repository:
lostelf/unarxive_dense - Split:
train - Shards exported:
15 - Rows exported:
127353 - Generated at:
2026-04-12T19:26:45.835499+00:00
Suggested use
Use this dataset as a portable snapshot of the EviGraph-R retrieval index for reproducible experiments, offline analysis, or mirroring the vector store outside Qdrant.
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