Sequential parametric convex approximation algorithm for bilinear matrix inequality problem

The goal of this paper is to study algorithms for solving optimization problems subject to bilinear matrix inequalities (BMIs). This class of problems is known to be of great importance in engineering applications, for instance, control system designs. A main contribution is the development of a seq...

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Bibliographic Details
Published inOptimization letters Vol. 13; no. 4; pp. 741 - 759
Main Authors Lee, Donghwan, Hu, Jianghai
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2019
Subjects
Computational Intelligence
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Operations Research/Decision Theory
Optimization
Original Paper
Simulation
Non-convex
Semidefinite programming
Control design
Optimization
Bilinear matrix inequality
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Summary:The goal of this paper is to study algorithms for solving optimization problems subject to bilinear matrix inequalities (BMIs). This class of problems is known to be of great importance in engineering applications, for instance, control system designs. A main contribution is the development of a sequential convex optimization algorithm, where at each iteration step, a convex subproblem with linear matrix inequality (LMI) constraints is solved. The set of feasible points of the LMIs is a convex inner approximation of the set of feasible points of the BMI constraints around the current iteration point. Another contribution is the convergence proof of a subsequence of the iterations to a stationary point. Finally, an example of the static output-feedback controller design problem is given for comparative analysis.
ISSN:1862-4472
1862-4480
DOI:10.1007/s11590-018-1274-6