Nonsmooth Methods for Control Design with Integral Quadratic Constraints

We develop an optimization technique to compute local solutions to synthesis problems subject to integral quadratic constraints (IQCs). We use the fact that IQCs may be transformed into semi-infinite maximum eigenvalue constraints over the frequency axis and approach them via nonsmooth optimization methods. We develop a suitable spectral bundle method and prove its convergence in … Read more

On local convergence of the method of alternating projections

The method of alternating projections is a classical tool to solve feasibility problems. Here we prove local convergence of alternating projections between subanalytic sets A,B under a mild regularity hypothesis on one of the sets. We show that the speed of convergence is O$(k^{-\rho})$ for some $\rho\in(0,\infty)$. Citation Université de Toulouse, Institut de Mathématiques, december … Read more

Bundle method for non-convex minimization with inexact subgradients and function values

We discuss a bundle method to minimize non-smooth and non-convex locally Lipschitz functions. We analyze situations where only inexact subgradients or function values are available. For suitable classes of non-smooth functions we prove convergence of our algorithm to approximate critical points. Citation To appear in: Computational and Analytical Mathematics. Springer Proceedings in Mathematics Article Download … Read more

Joint minimization with alternating Bregman proximity operators

A systematic study of the proximity properties of Bregman distances is carried out. This investigation leads to the introduction of a new type of proximity operator which complements the usual Bregman proximity operator. We establish key properties of these operators and utilize them to devise a new alternating procedure for solving a broad class of … Read more

Computational experience with an interior point algorithm for large scale contact problems

In this paper we present an interior point method for large scale Signorini elastic contact problems. We study the case of an elastic body in frictionless contact with a rigid foundation. Primal and primal-dual algorithms are developed to solve the quadratic optimization problem arising in the variational formulation. Our computational study confirms the efficiency of … Read more