35 research outputs found
Exact Penalization and Necessary Optimality Conditions for Multiobjective Optimization Problems with Equilibrium Constraints
A calmness condition for a general multiobjective optimization problem
with equilibrium constraints is proposed. Some exact penalization properties for two classes of
multiobjective penalty problems are established and shown to be equivalent to the calmness condition.
Subsequently, a Mordukhovich stationary necessary optimality condition based on the
exact penalization results is obtained. Moreover, some applications to a multiobjective optimization
problem with complementarity constraints and a multiobjective optimization problem with
weak vector variational inequality constraints are given
Nonlinear Lagrangian for multiobjective optimization and applications to duality and exact penalization
Author name used in this publication: Yang, X. Q.2002-2003 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe
Optimization and Equilibrium Problems with Equilibrium Constraints in Infinite-Dimensional Spaces
The paper is devoted to applications of modern variational f).nalysis to the study of constrained optimization and equilibrium problems in infinite-dimensional spaces. We pay a particular attention to the remarkable classes of optimization and equilibrium problems identified as MPECs (mathematical programs with equilibrium constraints) and EPECs (equilibrium problems with equilibrium constraints) treated from the viewpoint of multiobjective optimization. Their underlying feature is that the major constraints are governed by parametric generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and can be handled by using an appropriate machinery of generalized differentiation exhibiting a rich/full calculus. The case of infinite-dimensional spaces is significantly more involved in comparison with finite dimensions, requiring in addition a certain sufficient amount of compactness and an efficient calculus of the corresponding sequential normal compactness (SNC) properties
About [q]-regularity properties of collections of sets
We examine three primal space local Hoelder type regularity properties of
finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and
uniform [q]-regularity as well as their quantitative characterizations.
Equivalent metric characterizations of the three mentioned regularity
properties as well as a sufficient condition of [q]-subregularity in terms of
Frechet normals are established. The relationships between [q]-regularity
properties of collections of sets and the corresponding regularity properties
of set-valued mappings are discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1309.700
A Review on Non-Linear Programming and Generalized Invexity
Over past few years the concept of NLPP and their related results based on generalized invexity has become one of the prominent and important areas of classical optimization This paper presents a brief review on such problems and their respective results in game theory continuous time programming multivariable optimization composite programming et