Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2011-016 (September 23, 2011)

On finite convergence of an explicit exchange method for convex semi-infinite programming problems with second-order cone constraints
by Shunsuke Hayashi, Liping Zhang, and Soon-Yi Wu

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We consider the convex semi-infinite programming problem with second-order cone constraints (for short, SOCCSIP). We propose an explicit exchange method for solving SOCCSIP, and prove that the algorithm terminates in a finite number of iterations under some mild conditions. In the analysis, the complementarity slackness condition with respect to second-order cones plays an important role. To deal with such complementarity conditions, we utilize the spectral factorization techniques in Euclidean Jordan algebra. We also show that the obtained output is an approximate optimum of SOCCSIP. We also report some numerical results involving the application to the robust optimization in the classical convex semi-infinite programming.