The Romanian Academy, Centre of Math. Statistics, Calea 13
Septembrie Nr. 13, 76100 Bucharest 5, Romania
Abstract. A nonlinear multiple objective programming problem is considered where functions involved are -semidifferentiable. By consireding the concept of weak minima, the Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions are obtained. Moreover, a result relative to sufficiency of optimality conditions is given. Wolfe and Mond-Weir type duality results are given in terms of the -semidifferentials of the functions. The duality results are given using concepts of generalized semilocally preinvex functions.
1991 Mathematics Subject Classification. 90C26, 90C29, 90C30, 49J52.
Key words and phrases. Multiple objective programming, weak minimum, optimality conditions, duality, generalized preinvex functions.