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On a problem of Bauschke and Borwein

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Dániel Virosztek

Functional Analysis · Submitted 5 Dec 2014

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

The authors' main claim "Is $D_f$ jointly convex if and only if $D_F$ is?" In this short note we provide a negative answer to this question.

how it is stated · asserted 1.00 read the record →

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arXiv ID1412.2602 (version 2)
Pith ID4H6PU4FG, Pith's permanent record of this paper and its review
CitationD\'aniel Virosztek. "On a problem of Bauschke and Borwein." arXiv:1412.2602 (2014). https://pith.science/paper/4H6PU4FG
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The compiled record

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.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,355 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.31 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.37 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Consider a differentiable convex function $f: \mathbb{R}^n \supset \mathrm{dom} f \rightarrow \mathbb{R}.$ The induced spectral function $F$ is given by $F=f \circ \lambda,$ where $\lambda: \mathbf{M}_n^{sa} \rightarrow \mathbb{R}^{n}$ is the eigenvalue map. Let us denote by $D_f$ and $D_F$ the Bregman distances associated with $f$ and $F,$ respectively. In the paper "Joint and separate convexity of the Bregman distance" written by H. Bauschke and J. Borwein the following open problem has been suggested. "Is $D_f$ jointly convex if and only if $D_F$ is?" In this short note we provide a negative answer to this question.

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 Consider a differentiable convex function $f: \mathbb{R}^n \supset \mathrm{dom} f \rightarrow \mathbb{R}.$ The induced spectral function $F$ is given by $F=f \circ \lambda,$ where $\lambda: \mathbf{M}_n^{sa} \rightarrow \mathbb{R}^{n}$ is the eigenvalue map. background 1.00 0.09 0.02 asserted 0.98
s1 Let us denote by $D_f$ and $D_F$ the Bregman distances associated with $f$ and $F,$ respectively. background 1.00 0.24 0.02 asserted 0.69
s2 In the paper "Joint and separate convexity of the Bregman distance" written by H. background 0.99 0.04 0.02 unclear 0.90
s3 Bauschke and J. Borwein the following open problem has been suggested. background 0.95 0.05 0.03 asserted 0.55
s4 "Is $D_f$ jointly convex if and only if $D_F$ is?" In this short note we provide a negative answer to this question. result 0.78 0.92 0.96 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.95 · evidence from proof or derivation 0.97.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

Consider a differentiable convex function $f: \mathbb{R}^n \supset \mathrm{dom} f \rightarrow \mathbb{R}.$ The induced spectral function $F$ is given by $F=f \circ \lambda,$ where $\lambda: \mathbf{M}_n^{sa} \rightarrow \mathbb{R}^{n}$ is the eigenvalue map. Let us denote by $D_f$ and $D_F$ the Bregman distances associated with $f$ and $F,$ respectively. In the paper "Joint and separate convexity of the Bregman distance" written by H. Bauschke and J. Borwein the following open problem has been suggested. "Is $D_f$ jointly convex if and only if $D_F$ is?" In this short note we provide a negative answer to this question.

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