Levels sets infimal convolution and level addition

Journal of Optimization Theory and Applications

Volumn 94, Issue 3, 1997, Pages 695-714

  Luc, D T ^a   Volle, M ^a  

^a UNIVERSITY OF AVIGNON   (France)

Author keywords

connected level set; Infimal convolution; level sum; quasi convex function

Indexed keywords

CONVOLUTION;

CONNECTED LEVEL SET; GLOBAL MINIMUM; INFIMAL CONVOLUTION; LEVEL SET; LEVEL SUM; PROPERTY; QUASICONVEX; QUASICONVEX FUNCTIONS; REAL LINE; SUFFICIENT CRITERION;

FUNCTIONS;

EID: 0031536481     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022657102069     Document Type: Article

References (21)

1. ORTEGA, J. M., and RHEINBOLDT, W. C., Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, New York, 1970.
2. ZANG, I., and AVRIEL, M., On Function Whose Local Minima Are Global, Journal of Optimization Theory and Applications, Vol. 16, pp. 183-190, 1975.
3. HORST, R., and TUY, H., Global Optimization, Springer Verlag, Berlin, Germany, 1990.
4. ZANG, I., CHOO, E. U., and AVRIEL, M., A Note on Functions Whose Local Minima Are Global, Journal of Optimization Theory and Applications, Vol. 18, pp. 555-559, 1976.
5. AVRIEL, M., and ZANG, I., Generalized Arcwise Connected Functions and Characterizations of Local-Global Minimum Properties, Working Paper No. 502/77, Tel-Aviv University, 1977.
6. MARTIN, D. H., Some Function Classes Closed under Infimal Convolution, Journal of Optimization Theory and Applications, Vol. 25, pp. 579-584, 1978.
7. ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
8. VOLLE, M., Contributions à la Dualité en Optimisation et à l'Epiconvergence, Thèse, University of Pau, 1986.
9. ELQORTOBI, A., Inf-Convolution Quasi-Convexe des Fonctionnelles Positives, Recherche Opérationnelle, Vol. 26, pp. 301-311, 1992.
10. SEEGER, A., and VOLLE, M., On a Convolution Operation Obtained by Adding Level-Sets: Classical and New Results, Operations Research, Vol. 29, pp. 131-154, 1995.
11. TRAORE, S., and VOLLE, M., Subdifferentiability, Lower Semicontinuity and Exactness of the Level Sum of Two Convex Functions on Locally Convex Spaces, Recent Developments in Optimization, Edited by R. Durier and C. Michelot, Lecture Notes in Economics and Mathematical Systems, Springer, Berlin, Germany, Vol. 429, pp. 346-356, 1995.
12. TRAORE, S., and VOLLE, M., On the Level Sum of Two Convex Functions on Banach Spaces, Journal of Convex Analysis, Vol. 3, pp. 141-151, 1996.
13. TRAORE, S., and VOLLE, M., Epiconvergence d'une Suite de Sommes en Mibeaux de Fonctions Convexes, Serdica Mathematical Journal, Vol. 22, pp. 293-306, 1996.
14. LUC, D. T., and PENOT, J. P., Convergence of Asymptotic Directions, Preprint, Université de Pau, 1995.
15. AUBIN, J. P., and FRANKOWSKA, H., Set-Valued Analysis, Birkhauser-Boston, Cambridge, Massachusetts, 1990.
16. KLEIN, E., and THOMPSON, A. C., Theory of Correspondences, Wiley, New York, New York, 1984.
17. DANTZIG, G. B., FOLKMAN, J., and SHAPIRO, N., On the Continuity of the Minimum Set of a Continuous Function, Journal of Mathematical Analysis and Applications, Vol. 17, pp. 519-548, 1967.
18. HIRIART-URRUTY, J. B., Images of Connected Sets by Semicontinuous Multifunction, Journal of Mathematical Analysis and Applications, Vol. 111, pp. 407-442, 1985.
19. PENOT, J. P., Conditioning Convex and Nonconvex Problems, Journal of Optimization Theory and Applications, Vol. 90, pp. 539-558, 1996.
20. CROUZEIX, J. P., Contribution à l'Etude des Fonctions Quasiconvexes, Thèse, University of Clermont-Ferrand II, 1977.
21. AVRIEL, M., DIEWERT, W. E., SCHAIBLE, S., and ZANG, I., Generalized Concavity, Plenum Press, New York, New York, 1988.