Sequential convex relaxation for convex optimization with bilinear matrix equalities

Conference paper (2016)

Authors

R. Doelman Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
M.H.G. Verhaegen Team Raf Van de Plas - Mechanical, Maritime and Materials Engineering
Research Group
Team Raf Van de Plas (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2016 R. Doelman, M.H.G. Verhaegen
DOI: https://doi.org/10.1109/ECC.2016.7810576
Optimisation Convex programming Linear matrix inequalities
More Info
expand_more

Published Date

2016

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Raf Van de Plas

Abstract

We consider the use of the nuclear norm operator, and its tendency to produce low rank results, to provide a convex relaxation of Bilinear Matrix Inequalities (BMIs). The BMI is first written as a Linear Matrix Inequality (LMI) subject to a bi-affine equality constraint and subsequently rewritten into an LMI subject to a rank constraint on a matrix affine in the decision variables. The convex nuclear norm operator is used to relax this rank constraint. We provide an algorithm that iteratively improves on the sum of the objective function and the norm of the equality constraint violation. The algorithm is demonstrated on a controller synthesis example.