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.新算法中信赖域半径采用一个新的自适应调节策略.算法在每步迭代中以R-函数变化的速率和当前迭代点的信息来调节信赖域半径的大小,克服了传统信赖域算法中没有充分利用当前迭代点的信息调节信赖域半径的缺点.新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,则沿此试探步方向进行非单调线搜索得到步长.算法有别于传统的信赖域算法,没有重解子问题,减少了计算量.在较少的条件下,证明了算法的全局收敛性和超线性收敛性.
In this paper,a filter non-monotone trust region algorithm based on a simple quadratic model is proposed for unconstrained optimization problems. The trust region radius is adjusted with a new self-adaptive strategy. At each iteration,the trust region radius is updated at a variable rate of R-function and the information at the current point,which overcomes a shortcoming,i. e. the information at the current point in the traditional trust region algorithms is not employed. When the trial step is not accepted,a filter technique is employed into the method,which makes the trial point of the trust region sub-problem to be taken more often. If the trial step is also rejected by the filter set,a step size is got by the non-monotonic line search along it,and a new iterative point is achieved.The algorithm doesn＇t resolve the trust region sub-problem,so the amount of computation is reduced. The global convergence and super-convergence of this method is presented under fewer conditions.
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
2015年第2期223-229,共7页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(11061011)
广西自然科学基金(2011GXNSFA018138)资助项目
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
收敛性
unconstrained optimization
non-monotonic trust region algorithm
filter
simple quadratic model
convergence
