Zeroth-Order Optimization on Subsets of Symmetric Matrices With Application to MPC Tuning

Abstract

This article provides a zeroth-order optimization framework for nonsmooth and possibly nonconvex cost functions with matrix parameters that are real and symmetric. We provide complexity bounds on the number of iterations required to ensure a given accuracy level for both the convex and nonconvex cases. The derived complexity bounds for the convex case are less conservative than available bounds in the literature since we exploit the symmetric structure of the underlying matrix space. Moreover, the nonconvex complexity bounds are novel for the class of optimization problems that we consider. The utility of the framework is evident in the suite of applications that use symmetric matrices as tu..