[图书][B] Variational analysis and applications

BS Mordukhovich - 2018 - Springer
Boris S. Mordukhovich Page 1 Springer Monographs in Mathematics Boris S. Mordukhovich
Variational Analysis and Applications Page 2 Springer Monographs in Mathematics Editors-in-Chief …

Nonsmooth semi-infinite multiobjective optimization problems

TD Chuong, DS Kim - Journal of Optimization Theory and Applications, 2014 - Springer
We apply some advanced tools of variational analysis and generalized differentiation to
establish necessary conditions for (weakly) efficient solutions of a nonsmooth semi-infinite …

Farkas' lemma: three decades of generalizations for mathematical optimization

N Dinh, V Jeyakumar - Top, 2014 - Springer
In this paper we present a survey of generalizations of the celebrated Farkas's lemma,
starting from systems of linear inequalities to a broad variety of non-linear systems. We focus …

Constraint qualifications for extended Farkas's lemmas and Lagrangian dualities in convex infinite programming

DH Fang, C Li, KF Ng - SIAM Journal on Optimization, 2010 - SIAM
For an inequality system defined by a possibly infinite family of proper functions (not
necessarily lower semicontinuous), we introduce some new notions of constraint …

Isolated and proper efficiencies in semi-infinite vector optimization problems

TD Chuong, JC Yao - Journal of Optimization Theory and Applications, 2014 - Springer
This paper deals with a nonsmooth semi-infinite multiobjective/vector optimization problem
(SIMOP, for short). We first establish necessary and sufficient conditions for (local) strongly …

Robust conjugate duality for convex optimization under uncertainty with application to data classification

GY Li, V Jeyakumar, GM Lee - Nonlinear Analysis: Theory, Methods & …, 2011 - Elsevier
In this paper we present a robust conjugate duality theory for convex programming problems
in the face of data uncertainty within the framework of robust optimization, extending the …

Optimality conditions for approximate Pareto solutions of a nonsmooth vector optimization problem with an infinite number of constraints

TQ Son, N Van Tuyen, CF Wen - Acta Mathematica Vietnamica, 2020 - Springer
In this paper, we present some new necessary and sufficient optimality conditions in terms of
Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization …

Constraint qualifications and optimality conditions for nonconvex semi-infinite and infinite programs

B Mordukhovich, TTA Nghia - Mathematical Programming, 2013 - Springer
The paper concerns the study of new classes of nonlinear and nonconvex optimization
problems of the so-called infinite programming that are generally defined on infinite …

Optimality conditions for a simple convex bilevel programming problem

S Dempe, N Dinh, J Dutta - … Differentiation in Optimization and Control: In …, 2010 - Springer
The problem to find a best solution within the set of optimal solutions of a convex
optimization problem is modeled as a bilevel programming problem. It is shown that …

Necessary and sufficient optimality conditions in DC semi-infinite programming

R Correa, MA López, P Pérez-Aros - SIAM Journal on Optimization, 2021 - SIAM
This paper deals with particular families of DC optimization problems involving suprema of
convex functions. We show that the specific structure of this type of function allows us to …