A randomized method for solving semidefinite programs

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 9, Issue PART 1, 2007, Pages 227-231

  Polyak, B T ^a   Shcherbakov, P S ^a  

^a TRAPEZNIKOV INSTITUTE OF CONTROL SCIENCES   (Russian Federation)

Author keywords

Center of mass; Linear matrix inequalities; Optimization; Random walk

Indexed keywords

LINEAR MATRIX INEQUALITIES; OPTIMIZATION; RANDOM PROCESSES; SIGNAL PROCESSING;

CENTER OF MASS; COEFFICIENT MATRIX; CONVEX BODY; HIT-AND-RUN ALGORITHMS; NORM-BOUNDED UNCERTAINTY; RANDOM WALK; RANDOMIZED METHOD; SEMIDEFINITE PROGRAMS;

ITERATIVE METHODS;

EID: 79961073187     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20070829-3-ru-4911.00037     Document Type: Conference Paper

References (12)

1. A. Ben-Tal and A. Nemirovski. On tractable approximations of uncertain linear matrix inequalities affected by interval uncertainty. SIAM J. Optimiz., 12(3):811-833, 2002.
2. D. Bertsimas and S. Vempala. Solving convex programs by random walks. J. ACM, 51(4):540-556, 2004.
3. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan. Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994.
4. X. Chen, K. Zhou, and J. Aravena. Fast construction of robustness degradation function. SIAM J. Control Optimiz., 46(6):1960-1971, 2004.
5. L. El-Ghaoui, F. Oustry, and H. Lebret. Robust solutions to uncertain semidefinite programs. SIAM J. Optimiz., 9(1):33-52, 1998.
6. L. Lovász. Hit-and-run mixes fast. Math. Progr., 86:443- 461, 1999.
7. Yu. Nesterov and A. Nemirovskii. Interior-Point Polynomial Algorithms in Convex Programming. SIAM, Philadelphia, 1994.
8. B. T. Polyak. Robust linear algebra and robust aperiodicity. In A. Rantzer and C. I. Byrnes, editors, Directions in Mathematical Systems Theory and Optimization, pages 249-260. Springer, 2003.
9. B. T. Polyak and P. S. Shcherbakov. The D-decomposition technique for linear matrix inequalities. Automat. Remote Control, 67(11):159-174, 2006.
10. J. Radon. Über eine Erweiterung des Begriffs der konvexen Functionen, mit einer Anwendung auf die Theorei der konvexen Körper. S.- B. Akad. Wiss. Wien, 125:241- 258, 1916.
11. R. L. Smith. Efficient Monte Carlo procedures for generating points uniformly distributed over bounded regions. Operations Research, 32(6):1296-1308, 1984.
12. R. Tempo, G. Calafiore, and F. Dabbene. Randomized Algorithms for Analysis and Control of Uncertain Systems, Springer-Verlag, London, 2005.