Characterization and approximation of the convex envelope of a function

Journal of Optimization Theory and Applications

Volumn 110, Issue 2, 2001, Pages 457-466

  Kadhi, F ^a   Trad, A ^b  

^a University of Sfax   (Tunisia)

^b FACULTÉ DES SCIENCES DE TUNIS   (Tunisia)

Author keywords

Approximation; Convex envelope; Convex programming; Optimization

Indexed keywords

APPROXIMATION; CONVEX ENVELOPE; CONVEX PROGRAMMING PROBLEMS; OPTIMISATIONS;

CONVEX OPTIMIZATION;

EID: 0035536771     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1017591716397     Document Type: Article

References (9)

1. 1. ROCKAFELLAR, T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
2. 2. BRIGHT, B., and CHIPOT, M., Approximated Convex Envelope of a Function, SIAM Journal on Numerical Analysis, Vol. 31, pp. 128-148, 1994.
3. 3. LUCET, Y., A Fast Computational Algorithm for the Legendre-Fenchel Transform, Computational Optimization and Applications, Vol. 6, pp. 27-57, 1996.
4. 4. BENOIST, J., and HIRIART-URRUTY, J. B., What Is the Subdifferential of the Closed Convex Hull of a Function?, SIAM Journal on Mathematical Analysis, Vol. 27, pp. 1661-1679, 1994.
5. 5. GRIEWANK, A., and RABIER, P. J., On the Smoothness of the Convex Envelope, Transaction of the American Mathematical Society, Vol. 322, pp. 691-709, 1990.
6. 6. BRÉZIS, H., Analyse Fonctionnelle: Théorie et Applications, Masson, Paris, France, 1983.
7. 7. RUDIN, W., Analyse Complexe et Réelle, Masson, Paris, France, 1977.
8. 8. VALENTINE, F. A., Convex Sets, McGraw-Hill, New York, NY, 1964.
9. 9. DACOROGNA, B., Introduction au Calcul des Variations, Presses Polytechniques et Universitaires Romandes, Lausanne, Switzerland, 1992.