一类带非单调线搜索的信赖域算法  

A NEW FAMILY OF TRUST REGION ALGORITHMS WITH A NONMONOTONE LINE SEARCH TECHNIQUE

作　　者：庞善民[1] 陈兰平[1] 

机构地区：[1]首都师范大学数学科学学院,北京100048

出　　处：《计算数学》2011年第1期48-56,共9页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.60972140)资助

摘　　要：通过将非单调Wolfe线搜索技术与传统的信赖域算法相结合,我们提出了一类新的求解无约束最优化问题的信赖域算法.新算法在每一迭代步只需求解一次信赖域子问题,而且在每一迭代步Hesse阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下,证明了算法的全局收敛性和强收敛性.数值试验表明新算法继承了非单调技术的优点,对于求解某些优化问题具有重要意义.We propose a new family of trust region algorithms for unconstrained optimization problems which is combining traditional trust region method with a nonmonotone Wolfe line search technique. The new algorithm solves the trust region subproblem only once at each iteration, furthermore, the matrix approximation to the Hessian simultaneously sat- isfies the quasi-Newton condition at each iteration and maintains its positive definiteness. Under certain conditions, the global convergence and strong global convergence of the algorithm are proved. Numerical results show that the algorithm inherits the advantages of the nonmonotone schemes and is meaningful to some optimization problems.

关 键 词：无约束最优化 信赖域方法 非单调线搜索 全局收敛 

分 类 号：O224[理学—运筹学与控制论]