OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION  

作　　者：Tadeusz ANTCZAK 

机构地区：[1]Faculty of Mathematics and Computer Science,University of Lodz,Banacha 22,90-238 Lodz,Poland

出　　处：《Acta Mathematica Scientia》2017年第4期1133-1150,共18页数学物理学报（B辑英文版）

摘　　要：In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

关 键 词：nonsmooth multiobjective programming problem with the multiple interval- objective function Fritz John necessary optimality conditions Karush-Kuhn- Tucker necessary optimality conditions （weakly） LU-efficient solution Mond- Weir duality 

分 类 号：O221.6[理学—运筹学与控制论]