鲁棒多目标优化问题ε-拟弱有效解的最优性条件  

Optimality conditions forε-quasi-weakly efficient solutions of robust multiobjective optimization problem

作　　者：李梦恩 韩有攀[1] LI Mengen;HAN Youpan(School of Science,Xi’an Polytechnic University,Xi’an 710600,China)

机构地区：[1]西安工程大学理学院,西安710600

出　　处：《延边大学学报（自然科学版）》2022年第3期196-204,共9页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金(11501434);陕西省自然科学基金(2022JQ006)。

摘　　要：研究了约束函数带有不确定因素的多目标鲁棒优化问题的最优性条件.首先,利用变分分析的工具(最大值函数的次微分、中值不等式、极限次微分的和规则等)建立不确定多目标优化问题的鲁棒ε拟弱有效解的最优性必要条件;然后,在伪拟广义凸性的假设下,给出了该问题的最优性充分条件;最后,用实例证明了相关结论的正确性.The optimality conditions for multiobjective robust optimization problems with uncertain constraints are studied.Firstly,the necessary optimality conditions for robustε-quasi-weakly efficient solutions of uncertain multiobjective optimization problems are established by using modern variational analysis tools(the subdifferential of maximum function,median inequality,and the sum rule of limit subdifferential etc.).Then,under the assumption of pseudo quasi generalized convexity,the sufficient condition of optimality for the problem is given.Finally,an example is given to prove the correctness of relevant conclusions.

关 键 词：多目标优化 最优性条件 鲁棒ε拟弱有效解 次微分 广义凸性 

分 类 号：O221.6[理学—运筹学与控制论]