不等式约束优化一个基于滤子思想的广义梯度投影算法  

A GENERALIZED GRADIENT PROJECTION METHOD BASED ON THE IDEA OF FILTER FOR INEQUALITY CONSTRAINED OPTIMIZATION

作　　者：简金宝[1,2] 马鹏飞[3] 徐庆娟[4] 

机构地区：[1]玉林师范学院数学与信息科学学院,广西玉林537000 [2]广西大学数学与信息科学学院,南宁530004 [3]上海大学理学院,上海200444 [4]广西师范学院数学与信息科学学院,南宁530001

出　　处：《计算数学》2013年第2期205-214,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金(11271086);广西自然科学基金(2011GXNSFD018022);广西高校人才小高地建设创新团队资助计划

摘　　要：讨论非线性不等式约束优化问题,借鉴于滤子算法思想,提出了一个新型广义梯度投影算法.该方法既不使用罚函数又无真正意义下的滤子.每次迭代通过一个简单的显式广义投影法产生搜索方向,步长由目标函数值或者约束违反度函数值充分下降的Armijo型线搜索产生.算法的主要特点是:不需要迭代序列的有界性假设;不需要传统滤子算法所必需的可行恢复阶段;使用了ε积极约束集减小计算量.在合适的假设条件下算法具有全局收敛性,最后对算法进行了初步的数值实验.In this paper, optimization problems with nonlinear inequality constraints are discussed. Based on the idea of the filter algorithm, a new generalized gradient projection algorithm is proposed. The proposed method uses neither a penalty function, nor a strict filter. At each iteration of the proposed algorithm, the search direction is yield by just on explicit generalized gradient projection. The step-size is selected such that either the value of the objective function or the measure of the constraint violations is sufficiently reduced by a Armijo line search technique. The main properties of the proposed algorithm as follows： don＇t need to assume the boundness of iteration sequence; don＇t need any restoration phase which is necessary for filter methods; the scale and the computation cost are further decreased by using the z-active set. The algorithm is globally convergent under suitable assumptions. Finally, some elementary numerical experiments are reported.

关 键 词：约束优化 滤子 广义梯度投影 算法 全局收敛性 

分 类 号：O224[理学—运筹学与控制论]