New Lagrangian dual global optimization algorithm for solving bilinear matrix inequalities

International Journal of Robust and Nonlinear Control

Volumn 10, Issue 7, 2000, Pages 571-578

  Tuan, H D ^a   Apkarian, P ^b   Nakashima, Y ^c  

^a TOYOTA TECHNOLOGICAL INSTITUTE   (Japan)

^b ONERA   (France)

^c Tokyo Institute of Technology   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; CONVERGENCE OF NUMERICAL METHODS; OPTIMIZATION; SET THEORY;

BILINEAR MATRIX INEQUALITIES (BMI); LAGRANGIAN DUAL GLOBAL OPTIMIZATION;

MATRIX ALGEBRA;

EID: 0033703243     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. Toker O, Ozbay H. On the NP-hardness of solving bilinear matrix inequalities and simultaneous stabilization with static output feedback. Proceedings of ACC 1995; 2525-2526.
2. Goh KC, Safonov MG, Papavassilopoulos GP. A global optimization approach for the BMI problem. Journal of Global Optimization 1995; 7:365-380.
3. McCormick, GP. Computability of global solutions to factorable nonconvex programs: part I-convex underestimating problems. Mathematical Programming 1976; 10:147-175.
4. Al-Khayyal FA, Falk JE. Jointly constrained biconvex programming. Mathematics of Operation Research 1993; 8:237-286.
5. Horst R, Tuy H. Global Optimization: Deterministic Approaches (3rd edn). Springer: Berlin, 1996.
6. Sherali HD, Alameddine A. A new reformulation-linearization technique for bilinear programming problems. Journal of Global Optimization 1992; 2:379-410.
7. Al-Khayyal FA. Jointly constrained bilinear programs and related problems: an overview. Computers and Mathematics with Applications 1990; 19:53-62.
8. Tuy H. Convex Analysis and Global Optimization. Kluwer: Dordrecht, 1998.
9. Fujioka H, Hoshijima K. Bounds for the BMI eigenvalues problems - A good lower bound and a cheap upper bound. Transactions of SICE 1997; 33:616-621.
10. Tuan HD, Apkarian P, Hosoe S, Tuy H. D.C. optimization approach to robust controls: the feasibility problem, Preprint 9601, Department of Electronic-Mechanical Engineering, Nagoya University, Japan, October 1996; International Journal of Control 2000; 73:89-104.
11. Beran E. Methods for optimization based fixed-order control design. PhD Thesis, Technical University of Denmark, 1997.
12. Beran E, Vandenberge L, Boyd S. A global BMI algorithm based on the generalized Benders decomposition. Proceedings of ECC, 1997.
13. Kawanishi M, Sugie T, Kanki H. BMI global optimization based on branch and bound method taking account of the property of local minima. Proceedings of CDC 1997; 781-786.
14. Konno H, Thach PT, Tuy H. Optimization on Low Rank Nonconvex Structures, Kluwer: Dordrecht, 1997.
15. Alizadeh F, Haeberly JP, Nayakkankuppam MV, Overton ML. SDPPACK, version 0.8 beta, 1997.
16. Gahinet P, Nemirovski A, Laub AJ, Chilali M. LMI Control Toolbox. The Math-Works Inc., 1994.
17. Vandenberghe L, Boyd S. Semidefinite Programming. SIAM Review 1996; 38:49-95.
18. Nesterov Y, Nemirovskii, A. Interior Point Polynomial Methods for Convex Programming: Theory and Applications. SIAM: Philadelphia, PA, 1994.
19. Boyd S, ElGhaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics: Philadelphia, PA, 1994.
20. ∞ control. International Journal of Robust and Nonlinear Control 1994; 4:421-448.
21. Apkarian P, Tuan HD. Robust control via concave optimization: local and global algorithms. Proceedings of 37th CDC, 3855-3860. IEEE Transactions on Automatic Control, to appear.
22. Safonov MG, Goh KC, Ly JH. Control systems synthesis via bilinear matrix inequalities. Proceedings of the American Control Conference 1994; 45-49.