Symmetric duality for a class of nonlinear fractional programming problems. (English) Zbl 1014.90099
Summary: A pair of symmetric dual nonlinear fractional programming problem is presented and duality theorems are established under pseudoinvexity-pseudoincavity (and invexity-incavity, respectively) type assumptions on the kernel function. Special cases are particularly discussed to show that this paper extends some work appeared in this area.
Keywords:
nonlinear fractional programmingReferences:
| [1] | Dorn, W. S., A symmetric dual theorem for quadratic programs, J. Oper. Res. Soc. Japan, 2, 93-97 (1960) · Zbl 0095.14503 |
| [2] | Cottle, R. W., Symmetric dual quadratic programs, Quart. Appl. Math., 21, 237-243 (1963) · Zbl 0127.36802 |
| [3] | Dantzig, G. G.; Eisenberg, E.; Cottle, R. W., Symmetric dual nonlinear programs, Pacific J. Math., 15, 809-812 (1965) · Zbl 0136.14001 |
| [4] | Mond, B.; Weir, T., Generalized concavity and duality, (Schaible, S.; Ziemba, W. T., Generalized Concavity in Optimization and Economics (1981), Academic Press: Academic Press New York), 263-280 · Zbl 0538.90081 |
| [5] | Chandra, S.; Craven, B. D.; Mond, B., Symmetric dual fractional programming, Z. Oper. Res., 29, 59-64 (1985) · Zbl 0567.90092 |
| [6] | Mond B, B.; Schechter, M., Nondifferentiable symmetric duality, Bull. Austral. Math. Soc., 53, 177-188 (1996) · Zbl 0846.90100 |
| [7] | Chandra, S.; Craven, B. D.; Mond, B., Generalized concavity and duality with a square root term, Optimization, 16, 654-662 (1985) · Zbl 0575.49008 |
| [8] | Chandra, S.; Kumar, V., A note on pseudo-invexity and symmetric duality, European J. Oper. Res., 105, 626-629 (1998) · Zbl 0955.90125 |
| [9] | Craven, B. D., Lagrangian conditions and quasiduality, Bull. Austral. Math. Soc., 16, 325-339 (1977) · Zbl 0362.90106 |
| [10] | Hanson, M. A., On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl., 80, 545-550 (1981) · Zbl 0463.90080 |
| [11] | Kaul, R. N.; Kaur, S., Optimality criteria in nonlinear programming involving nonconvex functions, J. Math. Anal. Appl., 105, 104-112 (1985) · Zbl 0553.90086 |
| [12] | Mond, B., A symmetric dual theory for nonlinear programs, Quart. Appl. Math., 23, 265-269 (1965) · Zbl 0136.13907 |
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.
