IC/96/156 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS NEW GENERALIZATIONS OF FARKAS' THEOREM AND THEIR APPLICATIONS IN OPTIMAL CONTROL
نویسنده
چکیده
This paper deals with some new generalizations of Farkas' theorem for a class of set-valued mappings with arbitrary convex cones in infinite-dimensional Banach spaces. A modified Farkas' theorem with no closedness assumption is given. The generalized Gale alternative theorem in nonlinear programming is derived as an easy consequence. The results are applied to constrained controllability theory in Banach spaces as well as to some multiobjective optimization problem. MIRAMARE TRIESTE August 1996 On leave of absence from: Institute of Mathematics, Box 631, Bo Ho, Hanoi, Vietnam
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