非线性优化约束变尺度法新进展  

New progress of the variable metric method for nonlinear constrained optimization problems

作　　者：朱志斌[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2010年第5期523-527,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11061011);广西高校优秀人才资助项目([2009]156)

摘　　要：讨论了SQP算法与QP-free算法的研究背景及现状,介绍了它们的具体步骤及其相应的优缺点,构造了一个特殊的仅含等式约束的QP子问题,提出了相应的修正SQP方法,使之仍然具有求解不等式约束二次规划子问题的SQP方法相应的特点。构造一个特殊的线性方程组子问题,提出了相应的修正QP-free方法,减少了每步求解的子问题个数。Firstly,the research background and the current situation are discussed for the SQP algorithms and the QP-free algorithms.The specific steps and their corresponding advantages and disadvantages of two types of methods are described in detail.Then,against their shortcomings,a special equality constrained QP sub-problems is constructed,and the corresponding modified SQP method is proposed,such that it still has the corresponding features of SQP methods by solving inequality constrained quadratic programming sub-problems.A special sub-problem with linear equations is constructed,and corresponding modified QP-free method is proposed,such that the number of solving sub-problem is reduced in each step.

关 键 词：约束优化 SQP算法 QP-free算法 全局收敛 超线性收敛 

分 类 号：O211.1[理学—概率论与数理统计]