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Conditions for zero duality gap in convex programming

Borwein, Jonathan M. and Burachik, Regina S. and Yao, Liangjin (2014) Conditions for zero duality gap in convex programming. J. Convex and Nonlinear Analysis (15).

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    Abstract

    We introduce and study a new dual condition which characterizes zero duality gap in nonsmooth convex optimization. We prove that our condition is weaker than all existing constraint qualifications, including the closed epigraph condition. Our dual condition was inspired by, and is weaker 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.

    Item Type: Article
    Subjects: 46-xx Functional analysis
    47-xx Operator theory
    49-xx Calculus of variations and optimal control; optimization
    Faculty: UNSPECIFIED
    Depositing User: Dr Liangjin Yao
    Date Deposited: 13 Mar 2013 14:28
    Last Modified: 19 Nov 2014 22:14
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1465

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