Sequential convex relaxation for convex optimization with bilinear matrix equalities

Reinier Doelman, Michel Verhaegen

Research output: Chapter in Book/Conference proceedings/Edited volumeConference contributionScientificpeer-review

15 Citations (Scopus)
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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.
Original languageEnglish
Title of host publicationProceedings 2016 European Control Conference (ECC 2016)
EditorsAnders Rantzer, John Bagterp Jørgensen, Jakob Stoustrup
Place of PublicationPiscataway, NJ, USA
ISBN (Print)978-1-5090-2591-6
Publication statusPublished - 2016
Event2016 European Control Conference, ECC 2016: 15th annual European Control Conference - Aalborg, Denmark
Duration: 29 Jun 20161 Jul 2016


Conference2016 European Control Conference, ECC 2016
Abbreviated titleECC'16
Internet address

Bibliographical note

Accepted Author Manuscript


  • optimisation
  • convex programming
  • linear matrix inequalities


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