一种新的无约束优化线搜索算法  

A New Line Search Method for Unconstrained Optimization

作　　者：朱训芝[1] 唐焕文[1] 

机构地区：[1]大连理工大学应用数学系,辽宁大连116024

出　　处：《运筹与管理》2005年第5期18-23,共6页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(90103033)

摘　　要：在对各种有效的线搜索算法分析的基础上,给出了一种求解光滑无约束优化问题的新的线搜索算法。对于目标函数是二次连续可微且下有界的无约束优化问题,算法具有与Wolfe-Powell线搜索算法相同的理论性质。在每一步迭代中算法至多需要计算两次梯度,对于计算目标函数梯度花费较大的情形可以节省一定的计算量。数值试验表明本文算法是可行的和有效的。Based on the analysis for several kinds of line search methods, we propose a new line search algorithm for unconstrained optimization. It obtains the step-length after doing finite operations and has the same theoretical characters as the famous Wolf-Powell line search method for the minimization of the functions which are twice continuously differentiable and bounded below. Moreover, it requires two gradient evaluations at most in each of iteration and can save computation cost for the case when gradient evaluations are expensive. Numerical experiments show that the new algorithm in this paper is feasible and efficient.

关 键 词：运筹学 线性搜索 Wolfe-Powell准则 无约束优化 

分 类 号：O221.2[理学—运筹学与控制论]