Abstract convexity for nonconvex optimization duality

Title: Abstract convexity for nonconvex optimization duality
Creator: Nedic, A.; Ozdaglar, A.; Rubinov, Alex
Date: 2007
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/66122
Identifier: vital:644
Identifier: https://doi.org/10.1080/02331930701617379
Identifier: ISSN:0233-1934
Abstract: In this article, we use abstract convexity results to study augmented dual problems for (nonconvex) constrained optimization problems. We consider a nonincreasing function f that is lower semicontinuous at 0 and establish its abstract convexity at 0 with respect to a set of elementary functions defined by nonconvex augmenting functions. We consider three different classes of augmenting functions: nonnegative augmenting functions, bounded-below augmenting functions, and unbounded augmenting functions. We use the abstract convexity results to study augmented optimization duality without imposing boundedness assumptions.; C1
Publisher: Taylor and Francis
Relation: Optimization Vol. 56, no. 5-6 (2007), p. 655-674
Rights: Copyright Taylor and Francis
Rights: This metadata is freely available under a CCO license
Subject: 0103 Numerical and Computational Mathematics; Abstract convexity; Augmenting functions; Duality; Nonconvex optimisation
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