A Three‐Dimensional Filter‐Based SSDP Method for Nonlinear Semidefinite Programming With Its Applications

Abstract

Recently, there has been significant interest in filter methods for solving nonlinear problems. Extensions of these methods to nonlinear semidefinite programming (NLSDP) problems are described. A three‐dimensional filter sequential semidefinite programming (SSDP) algorithm with a feasible restoration phase is presented to efficiently solve NLSDPs with equality and matrix inequality constraints. In such an algorithm, the search direction is generated by solving a quadratic semidefinite subproblem. Reductions in the nonlinear objective function and constraint violation measure are ensured through a backtracking line search technique, three‐dimensional filter acceptance criteria, and a nonmonotonically sufficient descent condition. Under appropriate conditions, the global convergence of the proposed algorithm is established. Furthermore, we apply this algorithm to solve several applications, including the Rosen–Suzuki problem, the basic static output feedback problem, the Gaussian channel capacity problem, and the minimal eigenvalue problem. The experimental results demonstrate that it is both efficient and robust.