Separated continuous conic programming : Strong duality and an approximation algorithm

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

21 Scopus Citations
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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)2118-2138
Journal / PublicationSIAM Journal on Control and Optimization
Volume48
Issue number4
Publication statusPublished - 2009
Externally publishedYes

Abstract

Motivated by recent applications in robust optimization and in sign-constrained linear-quadratic control, we study in this paper a new class of optimization problems called separated continuous conic programming (SCCP). Focusing on a symmetric primal-dual pair, we develop a strong duality theory for the SCCP. Our idea is to use discretization to connect the SCCP and its dual to two ordinary conic programs. We show if the latter are strongly feasible and with finite optimal values, a condition that is readily verifiable, then the strong duality holds for the SCCP. This approach also leads to a polynomial-time approximation algorithm that solves the SCCP to any required accuracy. © 2009 Society for Industrial and Applied Mathematics.

Research Area(s)

  • Approximation algorithm, Conic programming, Continuous optimization, Duality