Optimality functions and lopsided convergence
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Authors
Royset, Johannes O.
Wets, Roger J-B.
Subjects
epi-Convergence
Lopsided convergence
Consistent approximations
Optimality functions
Optimality conditions
Lopsided convergence
Consistent approximations
Optimality functions
Optimality conditions
Advisors
Date of Issue
2015-10
Date
Publisher
Springer
Language
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.
Type
Article
Description
The article of record as published may be found at http://dx.doi.org/10.1007/s10957-015-0839-0
Series/Report No
Department
Operations Research
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
This material is based upon work supported in part by the US Army Research Laboratory and the US Army Research Office under Grant Numbers 00101-80683, W911NF-10-1-0246 and
W911NF-12-1-0273.
Funder
This material is based upon work supported in part by the US Army Research Laboratory and the US Army Research Office under Grant Numbers 00101-80683, W911NF-10-1-0246 and
W911NF-12-1-0273.
Format
19 p.
Citation
Journal of Optimization Theory and Applications, 19 p.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.