×

On harmonic convexity (concavity) and application to non-linear programming problems. (English) Zbl 1246.90122

Summary: The concept of harmonic convexity (concavity) is used to derive duality in non-linear programming problems. Moreover, the concept is extended to duality in fractional programming, symmetric and self-dual programs under weaker convexity conditions.

MSC:

90C26 Nonconvex programming, global optimization
90C30 Nonlinear programming
90C46 Optimality conditions and duality in mathematical programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bector, C.R., Bector, M.K., and Kalssen, J.E. (1997), Duality for a non-linear programming problem, utilitas mathematica, 11, 87-89.
[2] Bector, C.R., Chandra, S, and Husain, I. (1991), Second order duality for a minimax programming problem, Opsearch, Vol. 28, No. 4, 249-263. · Zbl 0755.90068
[3] Dantzig, G.B., Eisenberg, E. and Cottle, R.W. (1956), Symmetric duality in non-linear programming, Pacific Journ, Math 15 (3), 809-812. · Zbl 0136.14001
[4] Das, C. (1981), Generalized convexity and optimization problems, Mathematicki vesnik, 5 (18) (15), 349-359. · Zbl 0532.90080
[5] Das, C. (1975), Mathematical programming in complex space, Ph.D. dissertation, Sambalpur University.
[6] Das, C., Pattnaik, C. and Mishra, S. (2002) Harmonic convexity (concavity) and symmetric duality for non-linear programming problems, (accepted for publication in IJOMAS).
[7] Das, C. and Pradhan, P.K. (2002) Generalized convexity (concavity) and sufficient conditions for minimax problems, (accepted for publication in IJOMAS).
[8] Kilnger, Allen and Mangasarian, O.L. (1968), Logarithmic convexity and geometric programming, J. Math Anul Appl. 24 (2), 385-408.
[9] Mangasarian, O.L. (1965), Pseudoconvex functions, SIAMJ, control, S. 281-290. · Zbl 0138.15702
[10] Mond, B.; Weir, T.; Schaible, S. (ed.); Ziemba, WT (ed.), Generalized concavity and duality, 263-279 (1981), New York
[11] Nanda, S. (1988), Invex Generalization of some duality results, Opsearch, Vol. 25, No. 2, 105-111. · Zbl 0657.90091
[12] Schaible, S. (1976a), Duality in Fractional programming, A Unified Approach, Operations Research 24, 452-461. · Zbl 0348.90120
[13] Weir, T. (1990), On strong Pseudo convexity in non-linear programming and duality, Opsearch Vol. 27, No. 2, 117-121. · Zbl 0713.90058
[14] Wolfe, P. (1961), A duality theorem for non-linear programming, Quart-Appl. Math 19, 239-244. · Zbl 0109.38406
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.