Sequential convex relaxation for convex optimization with bilinear matrix equalities

Sequential convex relaxation for convex optimization with bilinear matrix equalities

Doelman, R. (TU Delft Team Raf Van de Plas)
Verhaegen, M.H.G. (TU Delft Team Raf Van de Plas)

Rantzer, Anders (editor)
Bagterp Jørgensen, John (editor)
Stoustrup, Jakob (editor)

2016

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.

optimisation
convex programming
linear matrix inequalities

http://resolver.tudelft.nl/uuid:0ef8bcbc-19e8-441c-834c-ef559d86683b

https://doi.org/10.1109/ECC.2016.7810576

IEEE, Piscataway, NJ, USA

978-1-5090-2591-6

Proceedings 2016 European Control Conference (ECC 2016)

2016 European Control Conference, ECC 2016, 2016-06-29 → 2016-07-01, Aalborg, Denmark

Accepted Author Manuscript

Institutional Repository

conference paper

© 2016 R. Doelman, M.H.G. Verhaegen