Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with application to Static Output Feedback
Optimization and Control
2011-09-19 v1 Systems and Control
Abstract
A novel optimization method is proposed to minimize a convex function subject to bilinear matrix inequality (BMI) constraints. The key idea is to decompose the bilinear mapping as a difference between two positive semidefinite convex mappings. At each iteration of the algorithm the concave part is linearized, leading to a convex subproblem.Applications to various output feedback controller synthesis problems are presented. In these applications the subproblem in each iteration step can be turned into a convex optimization problem with linear matrix inequality (LMI) constraints. The performance of the algorithm has been benchmarked on the data from COMPleib library.
Cite
@article{arxiv.1109.3320,
title = {Combining Convex-Concave Decompositions and Linearization Approaches for solving BMIs, with application to Static Output Feedback},
author = {Quoc Tran Dinh and Suat Gumussoy and Wim Michiels and Moritz Diehl},
journal= {arXiv preprint arXiv:1109.3320},
year = {2011}
}
Comments
22 pages