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Rank minimization approach for solving BMI problems with random search

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2 Author(s)
Ibaraki, S. ; Dept. of Precision Eng., Kyoto Univ., Japan ; Tomizuka, M.

Presents the rank minimization approach to solve general bilinear matrix inequality (BMI) problems. Due to the NP-hardness of BMI problems, no proposed algorithm that globally solves general BMI problems is a polynomial-time algorithm. We present a local search algorithm based on the semidefinite programming relaxation approach to indefinite quadratic programming, which is analogous to the well-known relaxation method for a certain-class of combinatorial problems. Instead of applying the branch and bound method for global search, a linearization-based local search algorithm is employed to reduce the relaxation gap. Furthermore, a random search approach is introduced along with the deterministic approach. Four numerical experiments are presented to show the search performance of the proposed approach

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American Control Conference, 2001. Proceedings of the 2001  (Volume:3 )

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