约束品性与非光滑多目标优化问题  

Constraint qualification and nonsmooth multiobjective optimization probems

作　　者：万轩 陈华峰 瞿先平 沈玉玲 WAN Xuan;CHEN Huafeng;QU Xianping;SHEN Yuling(Department of Foundation,Chongqing Teleconmmnication Polytechnic College,Chongqing 402247,China)

机构地区：[1]重庆电讯职业学院基础部,重庆402247

出　　处：《贵州师范大学学报（自然科学版）》2018年第3期61-64,共4页Journal of Guizhou Normal University：Natural Sciences

基　　金：重庆市教委科学技术研究项目(NO.KJ1605201)

摘　　要：考虑带不等式和集约束的非光滑多目标优化问题。首先利用Clarke方向导数、切锥、可达方向锥和线性化锥等工具引入广义Abadie约束品性和广义Kuhn-Tucker约束品性。进一步,分别在广义Abadie约束品性成立和广义Kuhn-Tucker约束品性成立这两种情况下,证明了Geoffrion真有效解是广义Kuhn-Tucker真有效解。We considered a nonsmooth multiobjective optimization problem with inequality constraints and set constraint. We first introduced the generalized Abadie constraint qualification and generalized Kuhn-Tucker constraint qualification in terms of Clarke directional derivative,tangent cone,the cone of attainable directions and linearized cone. Furthermore,we proved that Geoffrion proper efficient is generalized Kuhn-Tucker properly efficient under generalized Abadie constraint qualification holds or generalized Kuhn-Tucker constraint qualification holds.

关 键 词：非光滑多目标优化 广义Abadie约束品性 广义Kuhn-Tucker约束品性 Geoffrion真有效解 广义Kuhn-Tucker真有效解 

分 类 号：O221.2[理学—运筹学与控制论]