Efficient convex optimization for engineering design

Abstract

. Many problems in engineering analysis and design can be cast as convex optimization problems, often nonlinear and nondifferentiable. We give a high-level description of recently developed interior-point methods for convex optimization, explain how problem structure can be exploited in these algorithms, and illustrate the general scheme with numerical experiments. To give a rough idea of the efficiencies obtained, we are able to solve convex optimization problems with over 1000 variables and 10000 constraints in around 10 minutes on a workstation. Keywords. Optimization, numerical methods, linear programming, optimal control, robust control, convex programming, interior-point methods, FIR filter design, conjugate gradients 1. INTRODUCTION Many problems in engineering analysis and design can be cast as convex optimization problems, i.e., min f 0 (x) s.t. f i (x) 0; i = 1; : : : ; L; where the functions f i are convex. It is widely known that such problems have desirable properties,...