Beyond canonical DC programs: the single reverse polar problem

Bigi, Giancarlo and Frangioni, Antonio and Zhang, Qinghua (2011) Beyond canonical DC programs: the single reverse polar problem. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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Abstract

We propose a novel generalization of the canonical DC 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.<br />

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