Lagrangian approach to quasiconvex programing

Journal of Optimization Theory and Applications

Volumn 117, Issue 3, 2003, Pages 637-647

  Penot, J P ^a  

^a UNIVERSITÉ DE PAU ET DES PAYS DE L'ADOUR   (France)

Author keywords

Duality; Lagrangians; lower subdifferentials; mathematical programming; multipliers

Indexed keywords

LAGRANGE MULTIPLIERS;

DUALITY; LAGRANGIAN; LAGRANGIAN APPROACHES; LAGRANGIANS; LOW SUBDIFFERENTIAL; MATHEMATICAL PROGRAMMING PROBLEM; MULTIPLIER; QUASICONVEX; SIMPLE++; SUBDIFFERENTIALS;

MATHEMATICAL PROGRAMMING;

EID: 0038604795     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1023957924086     Document Type: Article

References (20)

1. MARTINEZ-LEGAZ, J. E., On Lower Subdifferentiable Functions, Trends in Mathematical Optimization, Edited by K. H. Hoffmann et al., International Series on Numerical Mathematics, Birkhäuser, Basel, Switzerland, Vol. 84, pp. 197-232, 1988.
2. PENOT, J. P., and VOLLE, M., On Quasiconvex Duality, Mathematics of Operations Research, Vol. 15, pp. 597-625, 1990.
3. LUENBERGER, D., Quasiconvex Programming, SIAM Journal on Applied Analysis, Vol. 16, pp. 1090-1095, 1968.
4. PENOT, J. P., and VOLLE, M., Surrogate Programming and Multipliers in Quasi-convex Programming, Preprint, University of Avignon, 1997, SIAM Journal on Optimization, to appear.
5. CROUZEIX, J. P., Conjugacy in Quasiconvex Analysis, Convex Analysis and Its Applications, Edited by A. Auslender, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 144, pp. 66-99, 1977.
6. PENOT, J. P., What is Quasiconvex Analysis?, Optimization, Vol. 47, pp. 35-110, 2000.
7. PENOT, J. P., Characterization of Solution Sets of Quasiconvex Programs, Journal of Optimization Theory and Applications, Vol. 117, pp. 627-636, 2003.
8. RUBINOV, A. M., HUANG, X. X., and YANG, X. Q., The Zero Duality Gap Property and Lower Semicontinuity of the Perturbation Functions, Preprint, University of Ballarat, Ballarat, Victoria, Australia.
9. MINOUX, M., Programmation Mathématique: Théorie et Algorithmes, Dunod, Paris, France, Vol. 1, 1983.
10. PSHENICHNYI, B. N., Necessary Conditions for an Extremum, Dekker, New York, NY, 1971.
11. PLASTRIA, F., Lower Subdifferentiable Functions and Their Minimization by Cutting Planes, Journal of Optimization Theory and Applications Vol. 46, pp. 37-54, 1985.
12. GUTIÉRREZ J. M., Infragradientes y Direcciones de Decrecimiento, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales, Madrid, Vol. 78, pp. 523-532, 1984.
13. PENOT, J. P., Duality for Radiant and Shady Programs, Acta Mathematica Vietnamica, Vol. 22, pp. 541-566, 1997.
14. RUBINOV, A., Abstract Convexity and Global Optimization, Kluwer, Dordrecht, Netherlands, 2000.
15. GREENBERG, H. P., and PIERSKALLA, W. P., Quasiconjugate Function and Surrogate Quality, Cahiers du Centre d'Etude de Recherche Operationnelle, Vol. 15, pp. 437-448, 1973.
16. PENOT, J. P., and QUANG, P. H., On the Cutting Plane Algorithm, Preprint, University of Pau, Pau, France, 1992.
17. CROUZEIX, J. P., Contribution à l'Etude des Fonctions Quasi-Convexes, Thèse d'Etat, University of Clermont II, 1977.
18. PENOT, J. P., Are Generalized Derivatives Useful for Generalized Convex Functions?, Generalized Convexity and Generalized Monotonicity, Edited by J. P. Crouzeix et al., Kluwer, Dordrecht, Netherlands, pp. 3-59, 1998.
19. PENOT, J. P., and ZALINESCU, C., Elements of Quasiconvex Subdifferential Calculus, Journal of Convex Analysis, Vol. 7, pp. 243-269, 2000.
20. BACHIR M., DANIILIDIS A., and PENOT J. P., Lower Subdifferentiability and Integration, Set-Valued Analysis, Vol. 10, pp. 89-108, 2002.