Results 11 to 20 of about 183 (174)

Attractors for Nonautonomous Multivalued Evolution Systems Generated by Time-Dependent Subdifferentials

Abstract and Applied Analysis, 2002
In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations.
Noriaki Yamazaki
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Min–sup-type zero duality gap properties for DC composite optimization problem

Journal of Inequalities and Applications, 2019
In this paper, we present min–sup-type zero duality gap properties for DC composite optimization problem with conic constraints. Using properties of the subdifferentials of involved functions, we introduce some new constraint qualifications.
Li Ping Tian, Dong Hui Fang
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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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Calculus Rules for V-Proximal Subdifferentials in Smooth Banach Spaces

Journal of Function Spaces, 2016
In 2010, Bounkhel et al. introduced new proximal concepts (analytic proximal subdifferential, geometric proximal subdifferential, and proximal normal cone) in reflexive smooth Banach spaces.
Messaoud Bounkhel
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Automatic differentiation rules for Tsoukalas–Mitsos convex relaxations in global process optimization

Digital Chemical Engineering, 2023
With increasing digitalization and vertical integration of chemical process systems, nonconvex optimization problems often emerge in chemical engineering applications, yet require specialized optimization techniques.
Yingwei Yuan, Kamil A. Khan
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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
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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.
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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, Elza M. Farkhi, Vera Roshchina   +2 more
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A Duality Framework for Mathematical Programs with Tangential Subdifferentials

Algorithms
The aim of this article is to study duality results for nonsmooth mathematical programs with equilibrium constraints in terms of tangential subdifferentials.
Vandana Singh, Shashi Kant Mishra, Abdelouahed Hamdi   +2 more
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Error Bound for Conic Inequality in Hilbert Spaces

Abstract and Applied Analysis, 2014
We consider error bound issue for conic inequalities in Hilbert spaces. In terms of proximal subdifferentials of vector-valued functions, we provide sufficient conditions for the existence of a local error bound for a conic inequality.
Jiangxing Zhu, Qinghai He, Jinchuan Lin
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