Abstract
We extend the duality theorems for a class of nondifferentiable problems with Mond-Weir type duals.
Similar content being viewed by others
References
Bhatia D (1970) A note on duality theorem for a nonlinear programming problem. Man Sci 16:604–606
Bhatia D and Kaul RN (1969) Nonlinear programming in complex space. J Math Anal Appl 28:144–152
Chandra S, Craven BD and Mond B (1985) Generalized concavity and duality with a square root term. Optimization 16, 5:653–662
Craven BD (1978) Mathematical Programming and Control Theory. Chapman and Hall, London
Craven BD (1981) Invex functions and constrained local minima, Bulletin of the Austral Math Soc 24:357–366
Fiacco AV and McCormick GP (1990) Nonlinear Programming: Sequential Unconstrained Minimization Techniques. SIAM, Philadelphia
Francis RL and Cabot AV (1972) Properties of a multifacility location problem involving Euclidean distances. Nav Res Log Quart 19:335–353
Hanson M (1981) On sufficiency of the Kuhn-Tucker conditions. J Math Anal Appl 80:545–550
Hanson M and Mond B (1982) Further generalizations of convexity in mathematical programming. J Inform Optim Sci 3:25–32
Jeyakumar V (1985) ρ-Convexity and second order duality. Utilitas Math 29:71–85
Mangasarian OL (1969) Nonlinear Programming. McGraw-Hill, New York
Mangasarian OL and Fromovitz S (1967) The Fritz John necessary optimality conditions in the presence of equality and inequality constraints. J Math Anal Appl 17:37–47
Mond B (1973) Nonlinear complex programming. J Math Anal Appl 43:633–641
Mond B (1973) On a duality theorem for a nonlinear programming problem. Oper Res 21:369–370
Mond B (1974) A class of nondifferentiable mathematical programming problems. J Math Anal Appl 46:169–174
Mond B (1983) Generalized convexity in mathematical programming. J Austral Math Soc Ser B 27:185–202
Mond B and Schechter M (1976) On a constraint qualification in a nondifferentiable programming problem. Naval Res Logist Quart 23:611–613
Mond B and Smart I (1989) Duality with invexity for a class of nondifferentiable static and continuous programming problems. J Math Anal Appl 141:373–388
Mond B and Weir T (1981) Generalized concavity and duality, in Generalized Concavity in Optimization and Economics, Edited by Schaible S and Ziemba WT. Academic Press, New York, 263–280
Preda V (1991) Optimality conditions for a class of mathematical programming problems. Rev Roum Math Pures et Appl (to appear)
Rani O (1973) A duality theorem for complex nonlinear programming. Opsearch 10:14–23
Rani O and Kaul RN (1973) Nonlinear programming in complex space. J Math Anal Appl 43:1–14
Sinha SM (1966) A duality theorem for nonlinear programming. Man Sci 12:385–390
Vial JP (1982) Strong convexity of sets and functions. J Math Econom 9:187–205
Vial JP (1983) Strong and weak convexity of sets and functions. Math Oper Res 8:231–259
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Preda, V. On generalized convexity and duality with a square root term. ZOR - Methods and Models of Operations Research 36, 547–563 (1992). https://doi.org/10.1007/BF01416245
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01416245