Didier Henrion There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called … Read more
We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming. Citation28 June 2007ArticleDownload View PDF
This document is an introduction to the Matlab package SDLS (Semi-Definite Least-Squares) for solving least-squares problems over convex symmetric cones. The package is shortly presented through the addressed problem, a sketch of the implemented algorithm, the syntax and calling sequences, a simple numerical example and some more advanced features. The implemented method consists in solving … Read more
We consider the class of nonlinear optimal control problems with all data (differential equation, state and control constraints, cost) being polynomials. We provide a simple hierarchy of LMI-relaxations whose optimal values form a nondecreasing sequence of lower bounds on the optimal value. Preliminary results show that good approximations are obtained with few moments. CitationLAAS report … Read more
We give a detailed numerical and theoretical analysis of a stabilization problem posed by V. Blondel in 1994. Our approach illustrates the effectiveness of a new gradient sampling algorithm for finding local optimizers of nonsmooth, nonconvex optimization problems arising in control, as well as the power of nonsmooth analysis for understanding variational problems involving polynomial … Read more
Using a moment interpretation of recent results on sum-of-squares decompositions of non-negative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve non-convex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to … Read more
GloptiPoly is a Matlab/SeDuMi add-on to build and solve convex linear matrix inequality relaxations of the (generally non-convex) global optimization problem of minimizing a multivariable polynomial function subject to polynomial inequality, equality or integer constraints. It generates a series of lower bounds monotonically converging to the global optimum. Numerical experiments show that for most of … Read more
A user-friendly free Matlab package for defining Linear Matrix Inequality (LMI) problems. It acts as an interface for the Self-Dual-Minimisation package SeDuMi developed by Jos F. Sturm. The functionalities of SeDuMi Interface are the following: (1) Declare an LMI problem. Five Matlab functions allow to define completely an LMI problem which can be characterised by … Read more