Optimality conditions for maximizations of set-valued functions
Tóm tắt
The maximization with respect to a cone of a set-valued function into possibly infinite dimensions is defined, and necessary and sufficient optimality conditions are established. In particular, an analogue of the Fritz John necessary optimality conditions is proved using a notion of derivative defined in terms of tangent cones.
Tài liệu tham khảo
Tanino, T., andSawaragi, Y.,Duality Theory in Multiobjective Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 509–529, 1979.
Corley, H. W.,Duality Theory for Maximizations with Respect to Cones, Journal of Mathematical Analysis and Applications, Vol. 84, pp. 560–568, 1981.
Corley, H. W.,Existence and Lagrangian Duality for Maximizations of Set-Valued Functions, Journal of Optimization Theory and Applications, Vol. 54, pp. 489–501, 1987.
Klein, K., andThompson, A. C.,Theory of Correspondences, John Wiley, New York, New York, 1984.
Zangwill, W. I.,Nonlinear Programming: a Unified Approach, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
Hogan, W. W.,Point-to-Set Maps in Mathematical Programming, SIAM Review, Vol. 15, pp. 591–603, 1973.
Robinson, S. M.,Generalized Equations and Their Solutions, Part 1: Basic Theory, Mathematical Programming Study, Vol. 10, pp. 128–141, 1979.
Clarke, F. H.,Optimization and Nonsmooth Analysis, John Wiley, New York, New York, 1983.
Corley, H. W.,On Optimality Conditions for Maximizations with Respect to Cones, Journal of Optimization Theory and Applications, Vol. 46, pp. 67–68, 1985.
Bazaraa, M. S., Goode, J. J., andNashed, M. Z.,On the Cones of Tangents with Applications to Mathematical Programming, Journal of Optimization Theory and Applications, Vol. 27, pp. 389–426, 1974.
Borwein, J.,Proper Efficient Points for Maximizations with Respect to Cones, SIAM Journal on Control and Optimization, Vol. 15, pp. 57–63, 1977.
Borwein, J.,Multivalued Convexity and Optimization: a Unified Approach to Inequality and Equality Constraints, Mathematical Programming, Vol. 13, pp. 183–199, 1977.
Guignard, M.,Generalized Kuhn-Tucker Conditions for Mathematical Programming Problems in a Banach Space, SIAM Journal on Control, Vol. 7, pp. 232–241, 1969.
Varaiya, P. P.,Nonlinear Programming in Banach Spaces, SIAM Journal on Applied Mathematics, Vol. 15, pp. 284–293, 1967.
Aubin, J. P., andEkeland, I.,Applied Nonlinear Analysis, John Wiley, New York, New York, 1984.
Hiriart-Urruty, J. B.,Tangent Cones, Generalized Gradients, and Mathematical Programming in Banach Spaces, Mathematics of Operations Research, Vol. 4, pp. 79–97, 1979.
Laurent, P. J.,Approximation et Optimisation, Hermann, Paris, France, 1972.
Edwards, R.,Functional Analysis: Theory and Applications, Holt, Rinehart and Winston, New York, New York, 1965.