×

Optimality conditions and duality in subdifferentiable multiobjective fractional programming. (English) Zbl 0796.90043

Summary: Fritz John and Kuhn-Tucker necessary and sufficient conditions for a Pareto optimum of a subdifferentiable multiobjective fractional programming problem are derived without recourse to an equivalent convex program or parametric transformation. A dual problem is introduced and, under convexity assumptions, duality theorems are proved. Furthermore, a Lagrange multiplier theorem is established, a vector-valued ratio-type Lagrangian is introduced, and vector-valued saddle-point results are presented.

MSC:

90C29 Multi-objective and goal programming
90C32 Fractional programming
49J52 Nonsmooth analysis
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Weir, T.,A Dual for a Multiobjective Fractional Programming Problem, Journal of Information and Optimization Sciences, Vol. 7, pp. 261-269, 1986. · Zbl 0616.90080
[2] Weir, T.,A Duality Theorem for a Multiobjective Fractional Optimization Problem, Bulletin of the Australian Mathematical Society, Vol. 34, pp. 415-425, 1986. · Zbl 0596.90089
[3] Singh, C.,A Class of Multiple-Criteria Fractional Programming Problems, Journal of Mathematical Analysis and Applications, Vol. 115, pp. 202-213, 1986. · Zbl 0599.90119
[4] Egudo, R. R.,Multiobjective Fractional Duality, Bulletin of the Australian Mathematical Society, Vol. 37, pp. 367-378, 1988. · Zbl 0647.90088
[5] Bector, C. R., Chandra, S., andSingh, C.,Duality in Multiobjective Fractional Programming, Proceedings of the International Workshop on Generalized Concavity Fractional Programming and Economic Applications, Pisa, Italy, 1988; Edited by A. Cambini, E. Castagnoli, L. Martein, P. Mazzoleni, and S. Schaible, Springer-Verlag, Berlin, Germany, pp. 232-241, 1988.
[6] Bector, C. R., Chandra, S., andDurga Prasad, M. V.,Duality in Pseudolinear Multiobjective Programming, Asia-Pacific Journal of Operational Research, Vol. 5, pp. 150-159, 1988. · Zbl 0715.90082
[7] Weir, T., andMond, B.,Generalized Convexity and Duality in Multiple Objective Programming, Bulletin of the Australian Mathematical Society, Vol. 39, pp. 287-299, 1989. · Zbl 0651.90083
[8] Kaul, R. N., andLyall, V.,A Note on Nonlinear Fractional Vector Maximization, Opsearch, Vol. 26, pp. 108-121, 1989. · Zbl 0676.90086
[9] Chandra, S., Craven, B. D., andMond, B.,Vector-Valued Lagrangian and Multiobjective Fractional Programming Duality, Numerical Functional Analysis and Optimization, Vol. 11, pp. 239-254, 1990. · Zbl 0689.90068
[10] Borwein, J. M.,Fractional Programming without Differentiability, Mathematical Programming, Vol. 11, pp. 283-190, 1976. · Zbl 0357.90054
[11] Lai, H. C., andHo, C. P.,Duality Theorem of Nondifferentiable Convex Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 50, pp. 407-420, 1986. · Zbl 0577.90077
[12] Kanniappan, P.,Necessary Conditions for Optimality of Nondifferentiable Convex Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 40, pp. 167-174, 1983. · Zbl 0488.49007
[13] Mangasarian, O. L.,Nonlinear Programming, McGraw Hill, New York, New York, 1969.
[14] Bazaraa, M. S., andShetty, C. M.,Nonlinear Programming Theory and Algorithms, John Wiley and Sons, New York, New York, 1979. · Zbl 0476.90035
[15] Sawaragi, S., Narayama, H., andTanino, T.,Theory of Multiobjective Optimization, Academic Press, New York, New York, 1985.
[16] Schechter, M.,More on Subgradient Duality, Journal of Mathematical Analysis and Applications, Vol. 71, pp. 251-162, 1979. · Zbl 0421.90062
[17] Yu, P. L.,Multiple Criteria Decision Making: Concepts, Techniques and Extensions, Plenum Press, New York, New York, 1985. · Zbl 0643.90045
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.