COMPUTING OPTIMAL LOCALLY CONSTRAINED STEPS
COMPUTING OPTIMAL LOCALLY CONSTRAINED STEPS
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DOI：
10.1137/0902016
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发表时间：
1981-01-01
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影响因子：
--
通讯作者：
GAY, DM
中科院分区：
文献类型：
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作者：
GAY, DM
在寻求解决一个无约束的最小化问题，一个经常计算步骤的基础上二次逼近的目标函数。选择这样的步骤的一个合理的方法是通过最小化qconstrained到当前节点的邻域。本文考虑椭球邻域，并提出了一种新的方法来处理某些计算细节时的Hessian的qis不定，特别注意一个特殊的情况下，可能会出现。本文提出的步长计算算法为处理负曲率问题提供了一种有吸引力的方法。该算法在非线性最小二乘求解NL2SOL中的应用结果令人满意。
In seeking to solve an unconstrained minimization problem, one often computes steps based on a quadratic approximationqto the objective function. A reasonable way to choose such steps is by minimizingqconstrained to a neighborhood of the current iterate. This paper considers ellipsoidal neighborhoods and presents a new way to handle certain computational details when the Hessian ofqis indefinite, paying particular attention to a special case which may then arise. The proposed step computing algorithm provides an attractive way to deal with negative curvature. Implementations of this algorithm have proved very satisfactory in the nonlinear least-squares solves NL2SOL.