Polynomial games and sum of squares optimization

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 2855-2860

  Parrilo, Pablo A ^a  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

NUMERICAL METHODS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

PAYOFF FUNCTIONS; POLYNOMIAL GAMES; SINGLE SEMI DEFLNITE PROGRAMMING; SQUARES OPTIMIZATION;

GAME THEORY;

EID: 39549103567     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.377261     Document Type: Conference Paper

References (20)

1. T. Başar and G. J. Olsder. Dynamic Noncooperative Game Theory. Number 23 in Classics in Applied Mathematics. SIAM, Philadelphia, PA, 1999.
2. D. Bertsimas and I. Popescu. Optimal inequalities in probability theory: a convex optimization approach. SIAM J. Optim., 15(3):780-804 (electronic), 2005.
3. L. Devroye. Nonuniform random variate generation. Springer-Verlag, New York, 1986.
4. M. Dresher, S. Karlin, and L. S. Shapley. Polynomial games. In Contributions to the Theory of Games, Annals of Mathematics Studies, no. 24, pages 161-180. Princeton University Press, Princeton, N. J., 1950.
5. D. Fudenberg and J. Tirole. Game theory. MIT Press, Cambridge, MA, 1991.
6. D. Gale and O. Gross. A note on polynomial and separable games. Pacific J. Math., 8:735-741, 1958.
7. I. Glicksberg and O. Gross. Notes on games over the square. In Contributions to the theory of games, vol. 2, Annals of Mathematics Studies, no. 28, pages 173-182. Princeton University Press, Princeton, N. J., 1953.
8. S. Karlin. Mathematical methods and theory in games, programming and economics. Vol. I: Matrix games, programming, and mathematical economics. Vol. II: The theory of infinite games. Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1959.
9. S. Karlin and L. Shapley. Geometry of moment spaces, volume 12 of Memoirs of the American Mathematical Society. AMS, 1953.
10. H. W. Kuhn and A. W. Tucker, editors. Contributions to the Theory of Games. Annals of Mathematics Studies, no. 24. Princeton University Press, Princeton, N. J., 1950.
11. J. B. Lasserre. Global optimization with polynomials and the problem of moments. SIAM J. Optim., 11(3):796-817, 2001.
12. R. B. Myerson. Game theory: analysis of conflict. Harvard University Press, Cambridge, MA, 1991.
13. Y. Nesterov. Squared functional systems and optimization problems. In J.B.G. Frenk, C. Roos, T. Terlaky, and S. Zhang, editors, High Performance Optimization, pages 405-440. Kluwer Academic Publishers, 2000.
14. P. A. Parrilo. Structured semidefinite programs and semi-algebraic geometry methods in robustness and optimization. PhD thesis, California Institute of Technology, May 2000. Available at http://resolver.caltech.edu/ CaltechETD:etd-05062004-055516.
15. P. A. Parrilo. Semidefinite programming relaxations for semialgebraic problems. Math. Prog., 96(2, Ser. B):293-320, 2003.
16. B. Reznick. Some concrete aspects of Hilbert's 17th problem. In Contemporary Mathematics, volume 253, pages 251-272. American Mathematical Society, 2000.
17. J.A. Shohat and J.D. Tamarkin. The Problem of Moments. American Mathematical Society Mathematical surveys, vol. II. American Mathematical Society, New York, 1943.
18. N. Z. Shor. Class of global minimum bounds of polynomial functions. Cybernetics, 23(6):731-734, 1987. (Russian orig.: Kibernetika, No. 6, (1987), 9-11).
19. N. D. Stein, A. E. Ozdaglar, and P. A. Parrilo. Separable and low-rank continuous games. MIT LIDS technical report, 2006.
20. V. L. Tiskin. Solution of polynomial games by the method of cut-offs. In Advances in game theory (Proc. Second All-Union Conf, Vilnius, 1971) (Russian), pages 69-72. Izdat. "Mintis", Vilnius, 1973.