×

zbMATH — the first resource for mathematics

On constraint qualification in multiobjective optimization problems: Semidifferentiable case. (English) Zbl 0915.90231
Summary: Some versions of constraint qualifications in the semidifferentiable case are considered for a multiobjective optimization problem with inequality constraints. A Maeda-type constraint qualification is given and Kuhn-Tucker-type necessary conditions for efficiency are obtained. In addition, some conditions that ensure the Maeda-type constraint qualification are stated.

MSC:
90C29 Multi-objective and goal programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Maeda, T., Constraint Qualifications in Multiobjective Optimization Problems: Differentiable Case, Journal of Optimization Theory and Applications, Vol, 80, pp. 483–500, 1994. · Zbl 0797.90083 · doi:10.1007/BF02207776
[2] Kuhn, H. W., and Tucker, A. W., Nonlinear Programming, Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, California, pp. 481–492, 1952.
[3] Yu, P. L., Multicriteria Decision Making: Concepts, Techniques, and Extensions, Plenum Press, New York, New York, 1985.
[4] Bazaraa, B. S., Goode, J. J., and Nashed, M. Z., On the Cones of Tangents with Applications in Mathematical Programming, Journal of Optimization Theory and Applications, Vol. 13, pp. 389–426, 1974. · Zbl 0259.90037 · doi:10.1007/BF00934938
[5] Varaiya, P. P., Nonlinear Programming in Banach Space, SIAM Journal on Applied Mathematics, Vol. 15, pp. 284–293, 1967. · Zbl 0171.18004 · doi:10.1137/0115028
[6] Laurent, J. P., Optimization et Approximation, Hermann, Paris, France, 1972.
[7] Kaul, R. N., and Kaur, S., Generalizations of Convex and Related Functions, European Journal of Operational Research, Vol. 9, pp. 369–377, 1982. · Zbl 0501.90090 · doi:10.1016/0377-2217(82)90181-3
[8] Ben-Israel, A., and Mond, B., What is Invexity?, Journal of the Australian Mathematical Society, Vol. 28B, pp. 1–9, 1986. · Zbl 0603.90119 · doi:10.1017/S0334270000005142
[9] Weir, T., and Mond, B., Preinvex Functions in Multiple-Objective Optimization, Journal of Mathematical Analysis and Applications, Vol. 136, pp. 29–38, 1988. · Zbl 0663.90087 · doi:10.1016/0022-247X(88)90113-8
[10] Suneja, S. K., and Gupta, S., Duality in Nonlinear Programming Involving Semilocally Convex and Related Functions, Optimization, Vol. 28, pp. 17–29, 1993. · Zbl 0818.90112 · doi:10.1080/02331939308843901
[11] Mangasarian, O. L., Nonlinear Programming, McGraw-Hill, New York, New York, 1969.
[12] Guignard, M., Generalized Kuhn-Tucker Conditions for Mathematical Programming, SIAM Journal on Control, Vol. 7, pp. 232–241, 1969. · Zbl 0182.53101 · doi:10.1137/0307016
[13] Isermann, H., Proper Efficiency and the Linear Vector Maximum Problem, Operations Research, Vol. 22, pp. 189–191, 1974. · Zbl 0274.90024 · doi:10.1287/opre.22.1.189
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.