Iterative Convex Overbounding Algorithms for BMI Optimization Problems

Abstract

This paper considers Iterative Convex Overbounding (ICO) techniques for Bilinear Matrix Inequality (BMI) problems. It is very common for BMIs to be present in multi-objective control, as well as many other optimization problems. Theoretically, ICO techniques guarantee monotonic convergence to a local optimum, and do not require the introduction of conservatism or relaxations. In this work, we propose an update to ICO which allows for improved results and a new convergence path. We also illustrate that ICO techniques are extensible to problems in which initial feasible design points are not known. Finally, we illustrate that ICO can be extended to matrix polynomial inequalities of arbitrary finite order. These ideas are demonstrated on a simple example.