Abstract
The present paper is concerned with the study of the optimality conditions for constrained multiobjective programming problems in which the data have locally Lipschitz Jacobian maps. Second-order necessary and sufficient conditions for efficient solutions are established in terms of second-order subdifferentials of vector functions.
Similar content being viewed by others
References
Jahn, J., Mathematical Theory of Vector Optimization in Partially-Ordered Spaces, Peter Lang, Frankfurt, Germany, 1985.
Yu, P.L., Multicriteria Decision Making: Concepts, Techniques, and Extensions, Plenum Press, New York, NY, 1985.
Luc, D.T., Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 319, 1989.
Giannessi, F., Mastroeni, G., and Pellegrini, L., On the Theory of Vector Optimization and Variational Inequalities: Image Space Analysis and Separation, Vector Variational Inequalities and Vector Equilibria, Edited by F. Giannessi, Kluwer Academic Publishers, London, England, pp. 153–216, 2000.
Guerraggio, A., Molho, E., and Zaffaroni, A., On the Notion of Proper Efficiency in Vector Optimization, Journal of Optimization Theory and Appli-cations, Vol. 82, pp. 1–21, 1994.
Khanh, P.Q., Proper Solutions of Vector Optimization Problems, Journal of Optimization Theory and Applications, Vol. 74, pp. 105–130, 1992.
Luc, D. T., and Schaible, S., On Efficiency and Generalized Concavity, Journal of Optimization Theory and Applications, Vol. 94, pp. 147–153, 1997.
Luc, D. T., On the Properly Efficient Points of Nonconvex Sets, European Jour-nal of Operations Research, Vol. 86, pp. 332–336, 1995.
Kuhn, H. W., and Tucker, F.H., Nonlinear Programming, Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, pp. 481–492, 1951.
Luc, D.T., Contingent Derivative of Set-Valued Maps and Applications to Vector Optimization, Mathematical Programming, Vol. 50, pp. 99–111, 1991.
Luc, D. T., and Malivert, C., Invex Optimization Problems, Bulletin of the Australian Mathematical Society, Vol. 46, pp. 47–66, 1992.
Craven, B.D., Nonsmooth Multiobjective Programming, Numerical Functional Analysis and Optimization, Vol. 10, pp. 49–64, 1989.
Luc, D.T., A Multiplier Rule for Multiobjective Programming Problems with Continuous Data, SIAM Journal on Optimization, Vol. 13, pp. 168–178, 2002.
Wang, S., Second-Order Necessary and Sufficient Conditions in Multiobjective Programming, Numerical Functional Analysis and Optimization, Vol. 12, pp. 237–252, 1991.
Bolintineau, S., and El maghri, M., Second-Order Efficiency Conditions and Sensitivity of Efficient Points, Journal of Optimization Theory and Applications, Vol. 98, pp. 569–592, 1998.
Aghezzaf, B., and Hachimi, M., Second-Order Optimality Conditions in Multiobjective Optimization Problems, Journal of Optimization Theory and Applications, Vol. 102, pp. 37–50, 1999.
Liu, L.P., The Second-Order Conditions of Nondominated Solutions for C 1,1 Generalized Multiobjective Mathematical Programming, Systems Sciences and Mathematical Sciences, Vol. 4, pp. 128–138, 1991.
Guerraggio, A., and Luc, D. T., Optimality Conditions for C 1,1 Vector Optim-ization Problems, Journal of Optimization Theory and Applications, Vol. 109, pp. 615–629, 2001.
Clarke, F.H., Optimization and Nonsmooth Analysis, Wiley, New York, NY, 1983.
Hiriart-urruty, J. B., Strodiot, J. J., and Nguyen, V.H., Generalized Hessian Matrix and Second-Order Optimality Conditions for Problems with C 1,1 Data, Applied Mathematics and Optimization, Vol. 11, pp. 43–56, 1984.
Klatte, D., and Tammer, K., On the Second-Order Sufficient Optimality Con-ditions for C 1,1 Optimization Problems, Optimization, Vol. 19, pp. 169–180, 1988.
Luc, D.T., Taylor's Formula for C k,1 Functions, SIAM Journal on Optimiz-ation, Vol. 5, pp. 659–669, 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Guerraggio, A., Luc, D. Optimality Conditions for C 1,1 Constrained Multiobjective Problems. Journal of Optimization Theory and Applications 116, 117–129 (2003). https://doi.org/10.1023/A:1022114319999
Issue Date:
DOI: https://doi.org/10.1023/A:1022114319999