Conditions for zero duality gap in convex programming

Title: Conditions for zero duality gap in convex programming
Creator: Borwein, Jonathan M.; Burachik, Regina S.; Yao, Liangjin
Relation: ARC
Relation: Journal of Nonlinear and Convex Analysis Vol. 15, Issue 1, p. 167-190
Relation: http://www.ybook.co.jp/online2/jncav15.html
Publisher: Yokohama Publishers
Resource Type: journal article
Date: 2014
Description: We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is less restrictive than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is less restrictive than, the so-called Bertsekas' condition for monotropic programming problems. We give several corollaries of our result and special cases as applications. We pay special attention to the polyhedral and sublinear cases, and their implications in convex optimization.
Subject: Bertsekas Constraint Qualification; Fenchel conjugate; Fenchel duality theorem; normal cone operator; inf-convolution; ε−subdifferential operator; subdifferential operator; zero duality gap
Identifier: http://hdl.handle.net/1959.13/1305557
Identifier: uon:21070
Identifier: ISSN:1345-4773
Language: eng
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