Optimization under non-convex Quadratic Matrix Inequality constraints with application to design of optimal sparse controller

Abstract

Matrix optimization problems that contain one or more non-convex quadratic matrix constraints are considered. An iterative solving method is proposed; at each iteration convex matrix subproblem is formulated and solved using standard Convex Optimization algorithms. Global convergence of the method is proven. Implementation of the method is especially simple if non-convex matrix constraints are concave. The method is applied for solving long-standing problem of the H∞ design with additional sparsity constraint or objective on the controller.