Beyond Canonical DC‐Optimization: The Single Reverse Polar Problem

Beyond Canonical DC‐Optimization: The Single Reverse Polar Problem

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Article ID: iaor20127250
Volume: 155
Issue: 2
Start Page Number: 430
End Page Number: 452
Publication Date: Nov 2012
Journal: Journal of Optimization Theory and Applications
Authors: , ,
Keywords: programming: convex
Abstract:

We propose a novel generalization of the Canonical Difference of Convex problem (CDC), and we study the convergence of outer approximation algorithms for its solution, which use an approximated oracle for checking the global optimality conditions. Although the approximated optimality conditions are similar to those of CDC, this new class of problems is shown to significantly differ from its special case. Indeed, outer approximation approaches for CDC need be substantially modified in order to cope with the more general problem, bringing to new algorithms. We develop a hierarchy of conditions that guarantee global convergence, and we build three different cutting plane algorithms relying on them.

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