基于简单二次函数模型的滤子非单调信赖域算法  

A filter non-monotone trust region algorithm with a simple quadratic model

作　　者：冯琳[1,2] 段复建[1] 和文龙[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 [2]安徽科技学院理学院,安徽凤阳233100

出　　处：《山东大学学报（理学版）》2012年第5期108-114,共7页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11061011);广西自然科学基金资助项目(2011GXNSFA018138)

摘　　要：对无约束最优化问题提出了一个基于简单二次函数模型的非单调滤子信赖域算法。算法在信赖域试探步不被接受时,采用滤子技术,增大试探步被接受的可能性;如果此试探步也不能被滤子集接受,则用固定的公式取搜索方向,并沿此搜索方向进行非单调Wolfe线搜索得到步长,从而产生新的迭代点。该算法不需要重解子问题,减少了计算量。在较少的条件下,证明了算法的全局收敛性。初步的数值试验表明了算法的有效性。A filter non-monotone trust region algorithm based on a simple quadratic model is proposed for unconstrained optimization problems. A filter technique is employed into the method, which makes the trial point of the trust region sub-problem be taken more often. If the trial step is also rejected by the filter set, a search direction is obtained by a fixed formula and a step size is obtained by the non-monotonic Wolfe line search, and thus a new iterative point is a- chieved. The algorithm does not resolve the trust region sub-problem, so the amount of computation is reduced. The global convergence of this new method is presented under fewer conditions. Preliminary numerical experiments show that the new method is effective.

关 键 词：无约束最优化 非单调信赖域算法 滤子 简单二次函数模型 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]