一种求解混合约束优化问题的半可行序列线性方程组滤子算法的全局收敛性  

Global Convergence of a Semi-feasible Sequential Systems of Linear Equations Filter Algorithm for Nonlinear Optimization Problems with General Constraits

作　　者：沈春根[1] 薛文娟[1] 濮定国[1] 

机构地区：[1]同济大学数学系

出　　处：《应用数学》2008年第1期114-122,共9页Mathematica Applicata

基　　金：国家自然基金(10571137);上海05优青项目基金(800008)资助

摘　　要：本文提出了一种半可行的序列线性方程组(SSLE)滤子方法.在文献[6]的基础上,将QP-free方法推广到混合约束优化问题,对不等式约束部分保持其可行性,而对等式约束部分用滤子方法处理,从而避免了罚参数的选取.本文提出的算法只需求解四个具有相同的非退化的系统矩阵的线性方程组以得到搜索方向.在一定程度上克服了SQP方法的缺点.另外,为了提高计算效率,算法中使用了χ-有效集.本文给出了该算法的全局收敛性证明.We propose a semi-feasible filter method, based on for solving general constrained nonlinear optimization problems, using the sequential systems of linear equations （SSLE）. In the algorithm,we keep the feasibility of the inquality constraints while for the e- quality ones,we use filter method to avoid using the penalty function. The new algorithm only needs to solve four systems of linear equations having the same nonsingular coefficient matrix. Furthermore,the X- active set procedure is used in order to improve the computational effect. The global convergence of our algorithm is given. And to some extent, the new algorithm can overcome the two shortcomings of the current SQP-type filter algorithms.

关 键 词：滤子 SSLE 线搜索 非线性约束优化 

分 类 号：O221.2[理学—运筹学与控制论]