NDLI: Optimality Functions and Lopsided Convergence

Content Provider	Springer Nature Link
Author	Royset, Johannes O. Wets, Roger J B
Copyright Year	2015
Abstract	Optimality functions pioneered by E. Polak characterize stationary points, quantify the degree with which a point fails to be stationary, and play central roles in algorithm development. For optimization problems requiring approximations, optimality functions can be used to ensure consistency in approximations, with the consequence that optimal and stationary points of the approximate problems indeed are approximately optimal and stationary for an original problem. In this paper, we review the framework and illustrate its application to nonlinear programming and other areas. Moreover, we introduce lopsided convergence of bifunctions on metric spaces and show that this notion of convergence is instrumental in establishing consistency of approximations. Lopsided convergence also leads to further characterizations of stationary points under perturbations and approximations.
Ending Page	983
Page Count	19
Starting Page	965
File Format	PDF
ISSN	00223239
e-ISSN	15732878
Journal	Journal of Optimization Theory and Applications
Issue Number	3
Volume Number	169
Language	English
Publisher	Springer US
Publisher Date	2015-11-09
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Optimality conditions, duality Theory of Computation epi-Convergence Set-valued and variational analysis Optimization Optimality conditions Engineering Optimality functions Consistent approximations Calculus of Variations and Optimal Control; Optimization Applications of Mathematics Operation Research/Decision Theory Lopsided convergence
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Control and Optimization Management Science and Operations Research

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