Results 21 to 30 of about 2,908 (221)
Subdifferentiation of integral functionals [PDF]
Mathematical Programming, 2017 The main scope of this paper is to investigate the way a nonsmooth subdifferential of a nonconvex integral function can be derived or estimated by means of the subdifferential of the corresponding integrand. Employing regularity hypotheses (a short discussion about various regularity notions can be found in the introduction), the results turn out to be
Emmanuel Giner, Jean-Paul Penot
openaire +4 more sources
Restricted Limiting Subdifferential and Applications
, 2018 International audienceThe aim of this note is to introduce a subdifferential in the spirit of the limiting Fréchet subdifferential. Chain rules are established and several properties are given.
Abderrahim Jourani +3 more
core +1 more source
Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure [PDF]
Journal of Optimization Theory and Applications, 2013 We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the DC structure of the function.
Robert Baier +2 more
openaire +2 more sources
Sufficient Optimality and Sensitivity Analysis of a Parameterized Min-Max Programming
Journal of Applied Mathematics, 2012 Sufficient optimality and sensitivity of a parameterized min-max programming with fixed feasible set are analyzed. Based on Clarke's subdifferential and Chaney's second-order directional derivative, sufficient optimality of the parameterized min-max ...
Huijuan Xiong, Yu Xiao, Chaohong Song
doaj +1 more source
ON TWO-SIDED UNIDIRECTIONAL MEAN VALUE INEQUALITY IN A FRÉCHET SMOOTH SPACE
Ural Mathematical Journal, 2023 The paper is devoted to a new unidirectional mean value inequality for the Fréchet subdifferential of a continuous function. This mean value inequality finds an intermediate point and localizes its value both from above and from below; for this reason ...
Dmitry V. Khlopin
doaj +1 more source
The Continuity of Subdifferential Mapping
Journal of Mathematical Analysis and Applications, 1997 The authors discuss continuity of the subdifferential mapping of the gauge of a bounded convex set with the origin an interior point and find a single-valuedness criterion for the mapping.
Wang, Jian-Hua, Nan, Chao-Xun
openaire +1 more source
On the Subdifferentiability of Convex Functions [PDF]
Proceedings of the American Mathematical Society, 1965 (Thus the subgradients of f correspond to the nonvertical supporting hyperplanes to the convex set consisting of all the points of E (DR lying above the graph of f.) The set of subgradients of f at x is denoted by of(x). If of(x) is not empty, f is said to be subdifferenticable at x.
Brøndsted, Arne, Rockafellar, R. T.
openaire +1 more source
AxiomsClarke subdifferential and directional derivative theories are well developed for real functions. However, the nonsmooth analysis framework for interval mappings is still incomplete.
Shexiang Hai, Yanmei Zhang
doaj +1 more source
Some notes on weak subdifferential
, 2017 Some necessary conditions for having nonempty weak subdifferential of a function are presented and the positively homogeneous of the weak subdifferential operator is proved. Necessary and sufficient conditions for achieving a global minimum of a
Ali Farajzadeh +2 more
core +1 more source
On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions [PDF]
, 2010 The Mordukhovich subdifferential is highly important in the variational and non-smooth analysis and optimization, but it may often be hard to calculate it. Here we propose a method of computing the Mordukhovich subdifferential of differences of sublinear
Elza Farkhi +5 more
core +1 more source