非光滑多目标最优化问题的强KKT条件

发布时间：2018-02-26 15:16

本文关键词： 非光滑多目标优化约束规格强KKT条件局部李普希兹函数 Clarke次微分　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：多目标优化问题的强KKT条件是相应于目标函数每个分量的拉格朗日乘子都大于零的KKT最优性条件,强KKT条件需要在约束规格的假设下才能成立.约束规格及强KKT条件方面的研究是多目标优化领域的重要研究课题,国内外的这方面的研究已经取得一系列重要结果.本文考虑含有不等式约束和任意集合约束,目标函数和约束函数都是局部李普希兹的非光滑多目标优化问题.利用Clarke次微分,相依锥和Clarke切锥,我们提出了两个新的广义Abadie约束规格,进而得到了一些新的有效解的强KKT最优性必要条件方面的结果.这些结果的证明主要运用了凸集的强分离定理.另外,我们还给出了本文所提出的约束规格以及其它一些广义Abadie约束规格之间关系的结果.
[Abstract]:The strong KKT condition for multiobjective optimization problem is the KKT optimality condition that the Lagrange multiplier of each component of the objective function is greater than zero. Strong KKT condition can only be established under the assumption of constraint specification. The research on constraint specification and strong KKT condition is an important research topic in the field of multi-objective optimization. A series of important results have been obtained in this field at home and abroad. In this paper, we consider inequality constraints and arbitrary set constraints. Objective functions and constraint functions are local Lipschitz's non-smooth multi-objective optimization problems. Using Clarke subdifferential, In this paper, we propose two new generalized Abadie constraint specifications for dependent cones and Clarke tangent cones, and obtain some results on the necessary and necessary conditions for strong KKT optimality of new efficient solutions. The proof of these results is mainly based on the strong separation theorems of convex sets. We also give the results of the relations between the constraint specifications and some other generalized Abadie constraint specifications presented in this paper.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O224

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