多目标优化问题proximal真有效解的最优性条件  

Optim ality Conditions for Proxim al Proper Efficiency in Multiobjective Optimization Problems

作　　者：李小燕[1] 高英[1] 

机构地区：[1]重庆师范大学数学学院,重庆400047

出　　处：《应用数学和力学》2015年第6期668-676,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11201511;11271391;11431004)~~

摘　　要：在广义凸性假设下,给出了集合proximal真有效点的线性标量化,并在此基础上证明了它与Benson真有效点和Borwein真有效点的等价性.将这些结果应用到多目标优化问题上,得到proximal真有效解的最优性条件.最后,利用proximal次微分,得到了proximal真有效解的模糊型最优性条件.First, linear scalarization of the proximal proper efficient points to a closed set was presented under the generalized convexity assumption, and the equivalency among the proximal proper efficiency, Benson proper efficiency and Borwein proper efficiency in multiobjective optimization problems was proved. Second, the optimality conditions for multiobjective optimization problems were obtained through application of these results to the problems. Finally, the fuzzy optimality conditions for the proximal proper efficient solutions were given with the proximal subdifferential.

关 键 词：proximal法锥 多目标优化 proximal真有效解 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]