NONMONOTONIC TRUST REGION ALGORITHM
NONMONOTONIC TRUST REGION ALGORITHM
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DOI：
10.1007/bf00939608
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发表时间：
1993-02-01
影响因子：
1.9
通讯作者：
ZHOU, FJ
中科院分区：
文献类型：
--
作者：
DENG, NY;XIAO, Y;ZHOU, FJ
提出了一种求解无约束优化问题的非单调信赖域方法。虽然该方法允许目标函数的值序列是非单调的，但在某些条件下，包括子问题的近似解的条件下，证明了与通常信赖域方法相似的收敛性。为了使解满足这些条件，还建立了一种求解子问题的算法。最后，给出了一些数值结果，表明非单调信赖域方法在梯度求值次数和函数求值次数方面都优于一般信赖域方法。
A nonmonotonic trust region method for unconstrained optimization problems is presented. Although the method allows the sequence of values of the objective function to be nonmonotonic, convergence properties similar to those for the usual trust region method are proved under certain conditions, including conditions on the approximate solutions to the subproblem. To make the solution satisfy these conditions, an algorithm to solve the subproblem is also established. Finally, some numerical results are reported which show that the nonmonotonic trust region method is superior to the usual trust region method according to both the number of gradient evaluations and the number of function evaluations.