An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control

Details An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control An Inner Convex Approximation Algorithm for BMI Optimization and Applications in Control

2012-02-24

arxiv.org/abs/1202.5488v1

Mathematics

Optimization and Control

7 pages and 3 tables. A shortened version is submitted to CDC2012, Feb 2012

Scientific paper

In this work, we propose a new local optimization method to solve a class of nonconvex semidefinite programming (SDP) problems. The basic idea is to approximate the feasible set of the nonconvex SDP problem by inner positive semidefinite convex approximations via a parameterization technique. This leads to an iterative procedure to search a local optimum of the nonconvex problem. The convergence of the algorithm is analyzed under mild assumptions. Applications in static output feedback control are benchmarked and numerical tests are implemented based on the data from the COMPLeib library.

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