Computing uniform convex approximations for convex envelopes and convex hulls

Journal of Convex Analysis

Volumn 15, Issue 3, 2008, Pages 635-654

  Laraki, R ^a   Lasserre, J B ^b  

^a ECOLE POLYTECHNIQUE   (France)

^b LAAS CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 48549086225     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (18)

1. G. A. Anastassiou: Moments in Probability and Approximation Theory, Longman, Harlow (1993).
2. J. Benoist, J.-B. Hiriart-Urruty: What is the subdifferential of the closed convex hull of a function?, SIAM J. Math. Anal. 27 (1996) 1661-1679.
3. A. Ben-Tal, A. Nemirovski: Lectures on Modern Convex Optimization, SIAM, Philadelphia (2001).
4. B. Brighi, M. Chipot: Approximated convex envelope of a function, SIAM J. Numer. Anal. 31 (1994) 128-148.
5. G. Choquet: Lectures on Analysis. I: Integration and Topological Vector Spaces, W. A. Benjamin, New York (1969).
6. J. W. Helton, V. Vinnikov: Linear matrix inequality representation of sets, Commun. Pure Appl. Math. 60 (2007) 654-674.
7. T. Jacobi, A. Prestel: Distinguished representations of strictly positive polynomials, J. Reine. Angew. Math. 532 (2001) 223-235.
8. J. H. B. Kemperman: Geometry of the moment problem, in: Moments in Mathematics, H. J. Landau (ed.), Proc. Symp. Appl. Math. 37, American Mathematical Society, Providence (1987) 16-53.
9. J. B. Kruskal: Two convex counterexamples: a discontinuous envelope function and a non differentiable nearest-point mapping, Proc. Amer. Math. Soc. 23 (1969) 697-703.
10. R. Laraki, W. D. Sudderth: The preservation of continuity and Lipschitz continuity by optimal reward operators, Math. Oper. Res. 29 (2004) 672-685.
11. R. Laraki: On the regularity of the convexification operator on a compact set, J. Convex Analysis 11 (2004) 209-234.
12. J. B. Lasserre: Global optimization with polynomials and the problem of moments, SIAM J. Optim. 11 (2001) 796-817.
13. A. S. Lewis, P. Parrilo, M. V. Ramana: The Lax conjecture is true, Proc. Amer. Math. Soc. 133 (2005) 2495-2499.
14. P. Parrilo, B. Sturmfels: Minimizing polynomial functions, in: Algorithmic and Quantitative Real Algebraic Geometry, S. Basu, L. Gonzalez-Vega (eds.), American Mathematical Society, Providence (2003) 83-100.
15. M. Putinar: Positive polynomials on compact semi-algebraic sets, Indiana Univ. Math. J. 42 (1993) 969-984.
16. R. T. Rockafellar: Convex Analysis, Princeton University Press, Princeton (1970).
17. K. Schmüdgen: The K-moment problem for compact semi-algebraic sets, Math. Ann. 289 (1991) 203-206.
18. L. Vandenberghe, S. Boyd: Semidefinite programming, SIAM Rev. 38 (1996) 49-95.