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向量极值问题的最优性条件及线性不等式约束二次规划问题的一种算法
The Optimality Conditions for Vector Extremum Problems & a Algorithm for Quadratic Programming with Linear Inequlities Constraints
【作者】 黄正刚;
【导师】 李泽民;
【作者基本信息】 重庆大学 , 计算数学, 2002, 硕士
【摘要】 本文主要讨论了抽象空间中向量优化问题的一些理论以及求解线性不等式约束二次规划问题的一种算法及其应用。 文章在Banach空间中界定了C-切锥的概念,并给出其有关性质,然后引入一种广义约束规格,从而得到了广义凸规划问题的最优性充分与必要条件;在线性拓扑空间中,给出集合(弱)有效点的重要性质,然后导出了约束向量极值问题像集的性质,在此基础上得到了原问题(弱)有效解存在的充分与必要条件;最后,在线性等式约束二次规划降维算法基础上,重点研究了线性不等式约束二次规划问题的一种算法,并对此算法的收敛性做出了一定分析,之后将该算法应用到求解一般的线性不等式约束非线性规划与多目标规划问题中,通过编制C++程序进行数值实验,表明此算法是实际可行﹑有效的
【Abstract】 In this thesis, some topics on vector optimization theory in abstract spaces are discussed, and a algorithm for quadratic programming problem with linear inequalities constraints is studied as well. In Banach space, the optimal concept of Contingent Cone is defined, and then, a generalized constrained qualification is given, thereafter, the optimal conditions of the differentiable optimization problem are obtained in Banach space; In linear toplogical space, a important property of (weak)efficient points of set is given , and then, the sufficient and the neccessory conditions of the vector extremum problem with constraint are obtained; Finally, this thesis gives a algorithm for quadratic programming problem with linear inequalities constraints, and its convergence is analysized in some degree, moreover, this algorithm is efficient compared with the results of numerical tests
【Key words】 Contingent cone; Generalized constrained qualification; Generalized convex programming; Optimal condition;
- 【网络出版投稿人】 重庆大学 【网络出版年期】2003年 02期
- 【分类号】O221.2
- 【被引频次】1
- 【下载频次】167