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Formulae for the Conjugate and the Subdifferential of the Supremum Function

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Pedro Pérez-Aros

Optimization and Control · Submitted 26 Dec 2017

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

The authors' main claim However, we show how to extend these results to arbitrary locally convex spaces without any qualification condition.

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arXiv ID1712.09318 (version 2)
Pith IDNKCGKISS, Pith's permanent record of this paper and its review
CitationPedro P\'erez-Aros. "Formulae for the Conjugate and the Subdifferential of the Supremum Function." arXiv:1712.09318 (2017). https://pith.science/paper/NKCGKISS
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,263 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.79 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

The aim of this work is to provide formulae for the subdifferential and the conjungate function of the supremun function over an arbitrary family of functions. The work is principally motivated by the case when data functions are lower semicontinuous proper and convex. Nevertheless, we explore the case when the family of functions is arbitrary, but satisfying that the biconjugate of the supremum functions is equal to the supremum of the biconjugate of the data functions. The study focuses its attention on functions defined in finite-dimensional spaces, in this case the formulae can be simplified under certain qualification conditions. However, we show how to extend these results to arbitrary locally convex spaces without any qualification condition.

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 The aim of this work is to provide formulae for the subdifferential and the conjungate function of the supremun function over an arbitrary family of functions. contribution 0.99 0.78 0.26 asserted 0.93
s1 The work is principally motivated by the case when data functions are lower semicontinuous proper and convex. background 0.96 0.29 0.04 asserted 1.00
s2 Nevertheless, we explore the case when the family of functions is arbitrary, but satisfying that the biconjugate of the supremum functions is equal to the supremum of the biconjugate of the data functions. contribution 0.96 0.88 0.09 asserted 0.97
s3 The study focuses its attention on functions defined in finite-dimensional spaces, in this case the formulae can be simplified under certain qualification conditions. limitation 0.57 0.66 0.06 asserted 0.88
s4 However, we show how to extend these results to arbitrary locally convex spaces without any qualification condition. contribution 0.67 0.94 0.23 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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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

The aim of this work is to provide formulae for the subdifferential and the conjungate function of the supremun function over an arbitrary family of functions. The work is principally motivated by the case when data functions are lower semicontinuous proper and convex. Nevertheless, we explore the case when the family of functions is arbitrary, but satisfying that the biconjugate of the supremum functions is equal to the supremum of the biconjugate of the data functions. The study focuses its attention on functions defined in finite-dimensional spaces, in this case the formulae can be simplified under certain qualification conditions. However, we show how to extend these results to arbitrary locally convex spaces without any qualification condition.

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