Representation of nonnegative convex polynomials

Archiv der Mathematik

Volumn 91, Issue 2, 2008, Pages 126-130

  Lasserre, Jean B ^a  

^a LAAS CNRS   (France)

Author keywords

Convex sets; Positive polynomials; Quadratic modules; Sums of squares

Indexed keywords

EID: 50849098824     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00013-008-2687-8     Document Type: Article

References (7)

1. J. W. HELTON AND J. NIE, Semidefinite representation of convex sets, Technical report, Mathematics Dept., University of California at San Diego, USA, 2007. arXiv:0705.4068.
2. J. B. LASSERRE AND T. NETZER, SOS approximations of nonnegative polynomials via simple high degree perturbations, Math. Z. 256, 99-112 (2006).
3. B. T. POLYAK, Introduction to Optimization, Optimization Software Inc., New York, 1987.
4. M. PUTINAR, Positive polynomials on compact semi-algebraic sets, Ind. Univ. Math. J. 42, 969-984 (1993).
5. C. SCHEIDERER, Positivity and sums of squares: A guide to recent results, in: Emerging Applications of Algebraic Geometry, M. Putinar and S. Sullivant (eds.), IMA Proceedings, Institute of Mathematics and Its Applications, Minneapolis, USA. To appear.
6. K. SCHMÜDGEN, The K-moment problem for compact semi-algebraic sets, Math. Ann. 289, 203-206 (1991).
7. M. SCHWEIGHOFER., On the complexity of Schmüdgen's Positivstellensatz, J. Complexity 20, 529-543 (2004).