广义拟向量变分不等式与拟近似解  

Generalized Quasi Vector Variational Inequalities and the Quasi-Approximate Efficient Solutions

作　　者：马圆圆 MA Yuan-yuan(School of Mathematical Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆工商大学学报（自然科学版）》2018年第5期56-59,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：重庆市基础科学与前沿技术研究重点项目(CSTC2015JCYJBX0029)

摘　　要：针对含有不等式约束、等式约束的多目标优化问题,其中目标函数和约束函数都是局部Lipschitz的,提出广义Stampacchia拟向量变分不等式的定义,以此作为工具去刻画近似拟有效解或近似弱拟有效解.利用两类新定义的广义凸函数,在合适的约束品性条件下,Kuhn-Tucker向量临界点,多目标优化的解与广义Stampacchia拟向量变分不等式在弱和强形式下的解之间的关系将会得到证明.A multiobjective problem with a feasible set defined by inequality, equality and set constraints is considered, where the objective and constraint functions are locally Lipschitz. A generalized Stampacchia quasi vector variational inequality is formulated as a tool to characterize approximate quasi- or weak quasi-efficient points. By using two new classes of generalized convexity functions, under suitable constraint qualifications, the relations between Kuhn-Tucker vector critical points, solutions to the multiobjective problem and solutions to the generalized Stampacchia vector variational inequality in both weak and strong forms are proved.

关 键 词：多目标问题 向量临界点 约束品性 拟向量变分不等式 

分 类 号：O224[理学—运筹学与控制论]