A Decomposition Algorithm for KYP-SDPs

Abstract

In this paper, a structure exploiting algorithm for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, where some of the constraints appear as complicating constraints is presented. A decomposition algorithm is proposed, where the structure of the problem can be utilized. In a numerical example, where a controller that minimizes the sum of the H 2 -norm and the H ∞ -norm is designed, the algorithm is shown to be faster than SeDuMi and the special purpose solver KYPD. Keywords: Optimization, Optimization Algorithms A Decomposition Algorithm for KYP-SDPs Rikard Falkeborn and Anders HanssonAbstract-In this paper, a structure exploiting algorithm for semidefinite programs derived from the Kalman-YakubovichPopov lemma, where some of the constraints appear as complicating constraints is presented. A decomposition algorithm is proposed, where the structure of the problem can be utilized. In a numerical example, where a controller that minimizes the sum of the H2-norm and the H∞-norm is designed, the algorithm is shown to be faster than SeDuMi and the special purpose solver KYPD.