消失约束数学规划问题的对偶性及一类光滑正则化方法

发布时间：2018-05-30 05:41

本文选题：消失约束数学规划 + Wolfe对偶　；参考：《桂林电子科技大学》2017年硕士论文

【摘要】：消失约束数学规划问题是一类用经典优化方法直接求解比较困难的约束优化问题,它在最优拓扑设计、机器人运动规划、电力经济调度和非线性最优控制中有着较广泛的应用。本文主要研究以下内容:首先研究消失约束数学规划问题的对偶性。我们主要给出S.K.Mishra,Vinay Singh,Vivek Laha等提出的Wolfe、Mond-Weir对偶的改进模型,使得模型中不涉及指标集的计算,同时给出相应的对偶性定理,并用例子解释对偶模型的合理性。其次研究求解消失约束数学规划问题的一类光滑正则化方法。该方法包含2013年Kanzow等提出的光滑正则化方法,同时在比Kanzow等提出的光滑正则化方法收敛性条件VC-LICQ弱的VC-MFCQ条件下,讨论了光滑正则化问题在可行点处成立MFCQ,还讨论了该类方法的收敛性,最后给出数值结果。
[Abstract]:Vanishing constrained mathematical programming problem is a kind of difficult constrained optimization problem which is solved directly by classical optimization method. It is widely used in optimal topology design, robot motion planning, power economic scheduling and nonlinear optimal control. The main contents of this paper are as follows: firstly, the duality of vanishing constraint mathematical programming problem is studied. We mainly give an improved model of Wolfemond-Weir duality put forward by S.K. Mishrag Vinay Singher Vivek Laha and others, so that the calculation of index set is not involved in the model. At the same time, we give the corresponding duality theorem and explain the rationality of the dual model with an example. Secondly, a class of smooth regularization methods for solving vanishing constrained mathematical programming problems is studied. This method includes the smooth regularization method proposed by Kanzow et al in 2013, and at the same time, under the VC-MFCQ condition that the convergence condition of the smooth regularization method proposed by Kanzow et al is weaker than that proposed by Kanzow et al., VC-LICQ is weak. In this paper, we discuss the problem of smooth regularization where MFCQ is set up at the feasible point, and discuss the convergence of this kind of method. Finally, the numerical results are given.
【学位授予单位】：桂林电子科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O221

【相似文献】