×

zbMATH — the first resource for mathematics

Second-order optimality conditions in multiobjective optimization problems. (English) Zbl 1039.90062
The authors develop second-order necessary and sufficient optimality conditions for multiobjective optimization problems with both equality and inequality constraints. First, the authors generalize the Lin fundamental theorem to second-order tangent sets; then, based on the above generalized theorem, the authors derive second-order necessary and sufficient conditions for efficiency.

MSC:
90C29 Multi-objective and goal programming
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lin, J. G., Maximal Vectors and Multiobjective Optimization, Journal of Optimization Theory and Applications, Vol. 18, pp. 41–64, 1976. · Zbl 0298.90056
[2] Maeda, T., Constraint Qualification in Multiobjective Optimization Problems: Differentiable Case, Journal of Optimization Theory and Applications, Vol. 80, pp. 483–500, 1994. · Zbl 0797.90083
[3] Marusciac, I., On Fritz John Type Optimality Criterion in Multiobjective Optimization, Analyse Numérique et Theorie de l’Approximation, Vol. 11, pp. 109–114, 1982. · Zbl 0501.90081
[4] Singh, C., Optimality Conditions in Multiobjective Differentiable Programming, Journal of Optimization Theory and Applications, Vol. 53, pp. 115–123, 1987. · Zbl 0593.90071
[5] Aghezzaf, B., Second-Order Necessary Conditions of Kuhn-Tucker Type in Multiobjective Optimization Problems, 12th International Conference on Multiobjective Criteria Decision Making, Fernuniversität Hagen, Hagen, Germany, 1995. · Zbl 0946.90075
[6] Wang, S., Second-Order Necessary and Sufficient Conditions in Multiobjective Programming, Numerical Functional Analysis and Optimization, Vol. 12, pp. 237–252, 1991. · Zbl 0764.90076
[7] Yu, P. L., Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions, Plenum Press, New York, New York, 1985.
[8] Kawasaki, H., Second-Order Necessary Conditions of the Kuhn-Tucker Type under New Constraint Qualification, Journal of Optimization Theory and Applications, Vol. 57, pp. 253–264, 1988. · Zbl 0621.90074
[9] Mangasarian, O. L., Nonlinear Programming, McGraw Hill, New York, New York, 1969.
[10] Ben-Tal, A., Second-Order and Related Extremality Conditions in Nonlinear Programming, Journal of Optimization Theory and Applications, Vol. 31, pp. 143–165, 1980. · Zbl 0416.90062
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.