×
Lai, H. C.; Lee, J. C.

On duality theorems for a nondifferentiable minimax fractional programming. (English) Zbl 1010.90080

J. Comput. Appl. Math. 146, No. 1, 115-126 (2002).
Summary: The optimality conditions of [H. C. Lai, J. C. Liu and K. Tanaka, J. Math. Anal. Appl. 230, No. 2, 311-328 (1999; Zbl 0916.90251)] can be used to construct two kinds of parameter-free dual models of nondifferentiable minimax fractional programming problems which involve pseudo-/quasi-convex functions. In this paper, the weak duality, strong duality, and strict converse duality theorems are established for the two dual models.

Cited in 1 Review
Cited in 34 Documents

MSC:

90C32 Fractional programming
26A51 Convexity of real functions in one variable, generalizations
49J35 Existence of solutions for minimax problems

Keywords:

minimax fractional problem; pseudo-convex functions; quasi-convex functions; duality; polyhedral cone

Citations:

Zbl 0916.90251
PDF BibTeX XML Cite
\textit{H. C. Lai} and \textit{J. C. Lee}, J. Comput. Appl. Math. 146, No. 1, 115--126 (2002; Zbl 1010.90080)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Bector, C.R.; Bhatia, B.L., Sufficient optimality conditions and duality for a minimax problem, Utilitas math., 27, 229-247, (1985) · Zbl 0574.90071
[2] Chandra, S.; Kumar, V., Duality in fractional minimax programming, J. austral. math. soc. ser. A, 58, 376-386, (1995) · Zbl 0837.90112
[3] Lai, H.C.; Liu, J.C., Duality for a minimax programming problem containing n-set functions, J. math. anal. appl., 229, 587-604, (1999) · Zbl 0922.90121
[4] Lai, H.C.; Liu, J.C., On minimax fractional programming of generalized convex set functions, J. math. anal. appl., 244, 442-465, (2000) · Zbl 1073.90543
[5] Lai, H.C.; Liu, J.C.; Tanaka, K., Necessary and sufficient conditions for minimax fractional programming, J. math. anal. appl., 230, 311-328, (1999) · Zbl 0916.90251
[6] Lai, H.C.; Liu, J.C.; Tanaka, K., Duality without a constraint qualification for minimax fractional programming, J. optim. theory appl., 101, 1, 109-125, (1999) · Zbl 0945.90078
[7] Liu, J.C.; Wu, C.S., On minimax fractional optimality conditions with invexity, J. math. anal. appl., 219, 21-35, (1998) · Zbl 0911.90317
[8] Liu, J.C.; Wu, C.S., On minimax fractional optimality conditions with (F,ρ)-convexity, J. math. anal. appl., 219, 36-51, (1998) · Zbl 0911.90318
[9] Liu, J.C.; Wu, C.S.; Sheu, R.L., Duality for fractional minimax programming, Optimization, 41, 117-133, (1997) · Zbl 0918.90127
[10] Schmittendorf, W.E., Necessary conditions and sufficient conditions for static minimax problems, J. math. anal. appl., 57, 683-693, (1977) · Zbl 0355.90066
[11] Weir, T., Pseudoconvex minimax programming, Utilitas math., 42, 234-240, (1992) · Zbl 0787.90069
[12] Yadav, S.R.; Mukherjee, R.N., Duality for fractional minimax programming problem, J. austral. math. soc. ser. B, 31, 484-492, (1990) · Zbl 0713.90083
[13] Zalmai, G.J., Optimality criteria and duality for a class of minimax programming problems with generalized invexity conditions, Utilitas math., 32, 35-37, (1987) · Zbl 0646.90092
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.