Results 21 to 30 of about 2,024 (222)
Local subdifferentials and multivariational inequalities in Banach and Frechet spaces [PDF]
Opuscula Mathematica, 2008 Some functional-topological concepts of subdifferential and locally subdifferential maps in Frechet spaces are established. Multivariational inequalities with an operator of the pseudo-monotone type, connected with subdifferential maps, are considered.
Pavlo O. Kasyanov +2 more
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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
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Subdifferential Calculus Using ϵ-Subdifferentials
Journal of Functional Analysis, 1993 AbstractIn applications of convex analysis it is important to be able to calculate the subdifferentials of various combinations of (proper and lower semicontinuous) convex functions, such as the sum of two such functions, or their inf-convolution ("epi-sum"), as well as the pre-composition of a convex function with an affine map or the "marginal ...
Hiriarturruty, J.B., Phelps, R.R.
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Axioms, 2022 In this paper, we introduce a second-order strong subdifferential of set-valued maps, and discuss some properties, such as convexity, sum rule and so on.
Yuwen Zhai, Qilin Wang, Tian Tang
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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
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Efficient Automatic Subdifferentiation for Programs with Linear Branches
Mathematics, 2023 Computing an element of the Clarke subdifferential of a function represented by a program is an important problem in modern non-smooth optimization.
Sejun Park
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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
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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
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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
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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
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