×
Singh, C.

Nondifferentiable fractional programming with Hanson-Mond classes of functions. (English) Zbl 0568.90091

J. Optimization Theory Appl. 49, 431-447 (1986).
A class of nonlinear fractional programming problems is considered in which the numerator of the objective function involves a finite sum of square roots of quadratic forms. Inequality and equality constraints are considered. Necessary and sufficient optimality conditions and weak, strong, and converse duality theorems are established in the framework of the Hanson-Mond classes of functions.

Cited in 7 Documents

MSC:

90C32 Fractional programming

Keywords:

nonlinear fractional programming; finite sum of square roots of quadratic forms; inequality and equality constraints; optimality conditions; duality theorems; Hanson-Mond classes of functions
Cite Review PDF
Full Text: DOI

References:

[1] Aggarwal, S. P., andSaxena, P. C.,A Class of Fractional Programming Problems, New Zealand Operational Research, Vol. 7, pp. 79-90, 1979.
[2] Hanson, M. A.,On Sufficiency of the Kuhn-Tucker Conditions, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 545-550, 1981. · Zbl 0463.90080 · doi:10.1016/0022-247X(81)90123-2
[3] Hanson, M. A., andMond, B.,Further Generalizations of Convexity in Mathematical Programming, Journal of Information and Optimization Sciences, Vol. 3, pp. 25-32, 1982. · Zbl 0475.90069
[4] Eisenberg, E.,Supports of a Convex Function, Bulletin of the American Mathematical Society, Vol. 68, pp. 192-195, 1962. · Zbl 0111.05903 · doi:10.1090/S0002-9904-1962-10741-1
[5] Bhatia, D.,A Note on Duality Theorem for a Nonlinear Programming Problem, Management Science, Vol. 16, pp. 604-606, 1970. · Zbl 0218.90053 · doi:10.1287/mnsc.16.9.604
[6] Mond, B.,A Class of Nondifferentiable Mathematical Programming Problems, Journal of Mathematical Analysis and Applications, Vol. 46, pp. 169-174, 1974. · Zbl 0276.90058 · doi:10.1016/0022-247X(74)90289-3
[7] Mangasarian, O. L.,Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
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.