A Lagrangian Multiplier Theorem of ε-weakly Efficient Solutions in Vector Optimization Problems with Set-valued Maps
Liao We · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2013
In this paper,we establish a Lagrangian multiplier theorem ofe-weakly efficient solutions in vector optimization problems with set-valued maps under the assumption of nearly cone-subconvexlike.Firstly,a necessary condition ofe-weakly efficient solutions is given in vector optimization problems with set-valued maps using an alternative theorem.Moreover,a sufficient and necessary condition ofe-weakly efficient solutions is given.Finally,under the assumption of nearly cone-subconvexlike,a Lagrangian multiplier theorem ofe-weakly efficient solutions is established for vector optimization problems with set-valued maps.The main results in this article extend the corresponding results in[6]to the approximate and meanwhile the convexity condition of[6]is reduced to the nearly cone-subconvexlike assumptions.