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On minimax theorems for lower semicontinuous functions in Hilbert spaces

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Ewa M. Bednarczuk, Monika Syga

Optimization and Control · Submitted 10 Jan 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space.

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arXiv ID1601.02239 (version 3)
Pith IDTGDPOSDG, Pith's permanent record of this paper and its review
CitationEwa M. Bednarczuk, Monika Syga. "On minimax theorems for lower semicontinuous functions in Hilbert spaces." arXiv:1601.02239 (2016). https://pith.science/paper/TGDPOSDG
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,876 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\Phi$-convex functions. These conditions are expressed in terms of abstract $\Phi$-subgradients.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. contribution 0.80 0.96 0.86 asserted 1.00
s1 The main tool is the theory of $\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\Phi$-convex functions. method 0.97 0.60 0.14 asserted 1.00
s2 These conditions are expressed in terms of abstract $\Phi$-subgradients. method 0.54 0.80 0.09 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • C citations
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We prove minimax theorems for lower semicontinuous functions defined on a Hilbert space. The main tool is the theory of $\Phi$-convex functions and sufficient and necessary conditions for the minimax equality to hold for $\Phi$-convex functions. These conditions are expressed in terms of abstract $\Phi$-subgradients.

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