Utilizing low rank properties when solving KYP-SDPs

Semidefinite programs and especially those derived from the Kalman-Yakubovich-Popov lemma are quite common in control applications. The solver KYPD is a dedicated solver for KYP-SDPs. It solves the optimization problem via the dual SDP and is an iterative solver. In each step a Hessian is formed and a linear system of equations is solved. The calculations can be performed much faster if we utilize sparsity and low rank structure. We show how to transform a dense optimization problem into a sparse one with low rank structure. A customized calculation of the Hessian is presented and investigated