On the Differentiability of Saddle and Biconvex Functions and Operators

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422014" target="_blank" >RIV/00216208:11320/20:10422014 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LdUcgreoZL" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=LdUcgreoZL</a>

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

On the Differentiability of Saddle and Biconvex Functions and Operators

Original language description

We strengthen and generalize results of J. M. Borwein [Partially monotone operators and the generic differentiability of convex-concave and biconvex mappings, Israel J. Math. 54 (1986) 42-50] and of A. Ioffe and R. E. Lucchetti [Typical convex program is very well posed, Math. Program. 104 (2005) 483-499] on Frechet and Gateaux differentiability of saddle and biconvex functions (and operators). For example, we prove that in many cases (also in some cases which were not considered before) these functions (and operators) are Frechet differentiable except for a G-null, s-lower porous set. Moreover, we prove these results for more general &quot;partially convex (up or down)&quot; functions and operators defined on the product of n Banach spaces.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GA18-11058S" target="_blank" >GA18-11058S: Generalized convexity in geometry and analysis</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Volume of the periodical

27

Issue of the periodical within the volume

2

Country of publishing house

DE - GERMANY

Number of pages

27

Pages from-to

705-731

UT code for WoS article

000548355600015

EID of the result in the Scopus database

2-s2.0-85076375069