Structured semidefinite representation of some convex sets

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2008, Pages 4797-4800

  Helton, J William ^a   Nie, Jiawang ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

SET THEORY;

CONVEX SET; RESTRICTIVE CONDITIONS;

LINEAR MATRIX INEQUALITIES;

EID: 62949235908     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2008.4738593     Document Type: Conference Paper

References (20)

1. J.W. Helton and J. Nie. Semidefinite Representation of Convex Sets. Submitted to Math. Prog.. http : //www.math.ucsd.edu/~njw.
2. J.W. Helton and J. Nie. Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets. Submitted to SIAM J. Optim.. http : //www.math.ucsd.edu/~njw.
3. Helton, J. W. and Vinnikov, V., Linear matrix inequality representation of sets, Communications On Pure & Appl Math, 60, p654-674, 5, 2007
4. M. Kojima, S. Kim and H. Waki. Sparsity in Sums of Squares of Polynomials. Math. Prog., Vol. 103 (1), 45-62 (2005).
5. J. B. Lasserre. Global optimization with polynomials and the problem of moments. SIAM J. Optim., 11(3): 796-817, 2001.
6. J. Lasserre. Convergent SDP-relaxations in polynomial optimization with sparsity. SIAM J. on Optim., Vol. 17, No. 3, pp. 822-843, 2006.
7. J. Lasserre. Convex sets with lifted semidefinite representation. Preprint, LAAS, 2006.
8. A. Nemirovskii. Advances in convex optimization: conic programming. Plenary Lecture, International Congress of Mathematicians (ICM), Madrid, Spain, 2006.
9. Y. Nesterov and A. Nemirovskii. Interior-point polynomial algorithms in convex programming. SIAM Studies in Applied Mathematics, 13. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1994.
10. J. Nie. Sum of squares method for sensor network localization. To appear in Computational Optimization and Applications.
11. J. Nie, J. Demmel and B. Sturmfels. Minimizing polynomials via sum of squares over the gradient ideal. Math. Prog., Series A, Vol. 106 (2006), No. 3, pp. 587-606.
12. J. Nie and J. Demmel. Minimum ellipsoid bounds for solutions of polynomial systems via sum of squares. Journal of Global Optimization, Vol. 33(2005), pp. 511-525.
13. J. Nie and J. Demmel. Sparse SOS relaxations for minimizing functions that are summations of small polynomials. Preprint, 2006. http://arxiv.org/abs/math/0606476.
14. J. Nie, P. Parrilo and B. Sturmfels. Semidefinite Representation of the k-Ellipse. IMA Volume 146: Algorithms in Algebraic Geometry (Eds. A. Dickenstein, F.-O. Schreyer, and A. Sommese), Springer, New York, 2008.
15. P. Parrilo. Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization. PhD thesis, California Institute of Technology, May 2000.
16. P. A. Parrilo and B. Stunnfels. Minimizing polynomial functions. In S. Basu and L. Gonzalez-Vega, editors, Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, volume 60 of DIMACS Series in Discrete Mathematics and Computer Science, pages 83-99. AMS, 2003.
17. PA. Parrilo. Exploiting structure in sum of squares programs. Proceedings for the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, 2003.
18. P.Parrilo. Exact semidefinite representation for genus zero curves. Talk at the Banff workshop "Positive Polynomials and Optimization", Banff, Canada, October 8-12, 2006.
19. B. Reznick. Extremal psd forms with few terms. Duke Math. J., 45(1978), No. 2, pp. 363-374.
20. H. Waki, S. Kim, M. Kojima and M. Muramatsu. Sums of Squares and Semidefinite Programming Relaxations for Polynomial Optimization Problems with Structured Sparsity. SIAM J. on Optim., Vol. 17 No. 1 pp. 218-242 (2006).