Results 181 to 190 of about 15,245 (222)

Approximations of Subdifferentials

2014
In practice, the computation of subdifferential is not an easy task. In this chapter, we first consider some families of set-valued mappings that can be used to approximate subdifferentials. Then we define the concept of a discrete gradient that can be used as an approximation of the subgradient at a given point.
Adil Bagirov, Napsu Karmitsa, Marko M. Mäkelä   +2 more
openaire   +1 more source

Subdifferential calculus without qualification conditions, using approximate subdifferentials: A survey

Nonlinear Analysis: Theory, Methods & Applications, 1995
The aim of this survey paper is to present calculus rules for the subdifferential \(\partial f\) of a convex function \(f\) constructed from other convex functions \(f_i\) by means of the main operations encountered in convex analysis, without any qualification conditions.
Hiriart-Urruty, J.-B., Moussaoui, M., Seeger, A., Volle, M.   +3 more
openaire   +2 more sources

Weak Convexity and Approximate Subdifferentials

Journal of Optimization Theory and Applications
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wim van Ackooij, Felipe Atenas, Claudia Sagastizábal   +2 more
openaire   +2 more sources

Variational Subdifferential for Quasiconvex Functions

Journal of Optimization Theory and Applications, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Subdifferentials with Autoconjugate Fitzpatrick Function

Set-Valued and Variational Analysis, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Das konvexe Subdifferential

2021
Das zentrale Werkzeug zur konkreten Umsetzung des Satzes von Lewis und Pang ist das Subdifferential einer konvexen Funktion, das das vorliegende Kapitel ausfuhrlich diskutiert. Wir sehen unter anderem, wie sich die einseitige Richtungsableitung einer konvexen Funktion und ihr Subdifferential wechselseitig auseinander konstruieren lassen, und dass sich ...
openaire   +1 more source

Limiting Subdifferential Calculus and Perturbed Distance Function in Riemannian Manifolds

Journal of Global Optimization, 2020
M. Farrokhiniya, A. Barani
semanticscholar   +1 more source

Infinitesimals and Subdifferentials

2002
The nonstandard methods of analysis have been applied to various fields of mathematics. In the present chapter we shall consider the use of infinitesimals in subdifferential calculus, one of the new branches of functional analysis which originated from evolution of the theory of extremal problems.
E. I. Gordon, A. G. Kusraev, S. S. Kutateladze   +2 more
openaire   +1 more source

Sigma-subdifferential and its application to minimization problem

Positivity (Dordrecht), 2020
Hui Huang, Chunyou Sun
semanticscholar   +1 more source

Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential

Journal of Global Optimization, 2020
S. Suzuki
semanticscholar   +1 more source