Approximations and Solution Estimates in Optimization
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Authors
Royset, Johannes O.
Subjects
epi-convergence
Attouch-Wets distance
epi-splines
solution stability
approximation theory
near-optimality
near-feasibility
rate of convergence
Attouch-Wets distance
epi-splines
solution stability
approximation theory
near-optimality
near-feasibility
rate of convergence
Advisors
Date of Issue
2016-04-06
Date
April 6, 2016
Publisher
Language
Abstract
Approximation is central to many optimization problems and the supporting theory pro-
vides insight as well as foundation for algorithms. In this paper, we lay out a broad framework for
quantifying approximations by viewing nite- and in nite-dimensional constrained minimization prob-
lems as instances of extended real-valued lower semicontinuous functions de ned on a general metric
space. Since the Attouch-Wets distance between such functions quanti es epi-convergence, we are able
to obtain estimates of optimal solutions and optimal values through estimates of that distance. In par-
ticular, we show that near-optimal and near-feasible solutions are effectively Lipschitz continuous with
modulus one in this distance. We construct a general class of approximations of extended real-valued
lower semicontinuous functions that can be made arbitrarily accurate and that involve only a nite
number of parameters under additional assumptions on the underlying metric space.
Type
Description
This paper is in review.
Series/Report No
Department
Operations Research (OR)
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
26 p.
Citation
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.