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Approximations and solution estimates in optimization.

Authors :
Royset, Johannes O.
Source :
Mathematical Programming. Aug2018, Vol. 170 Issue 2, p479-506. 28p.
Publication Year :
2018

Abstract

Approximation is central to many optimization problems and the supporting theory provides insight as well as foundation for algorithms. In this paper, we lay out a broad framework for quantifying approximations by viewing finite- and infinite-dimensional constrained minimization problems as instances of extended real-valued lower semicontinuous functions defined on a general metric space. Since the Attouch-Wets distance between such functions quantifies epi-convergence, we are able to obtain estimates of optimal solutions and optimal values through bounds of that distance. In particular, we show that near-optimal and near-feasible solutions are effectively Lipschitz continuous with modulus one in this distance. Under additional assumptions on the underlying metric space, we construct approximating functions involving only a finite number of parameters that still are close to an arbitrary extended real-valued lower semicontinuous functions. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
00255610
Volume :
170
Issue :
2
Database :
Academic Search Index
Journal :
Mathematical Programming
Publication Type :
Academic Journal
Accession number :
130550769
Full Text :
https://doi.org/10.1007/s10107-017-1165-0