An efficient trust region algorithm for minimizing nondifferentiable composite functions
An efficient trust region algorithm for minimizing nondifferentiable composite functions
复制标题
最小化不可微复合函数的有效信赖域算法
DOI：
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发表时间：
1989
期刊：
影响因子：
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通讯作者：
M. Fukushima
中科院分区：
文献类型：
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作者：
Eiki Yamakawa;M. Fukushima
本文提出了一种用于解决以下问题的信赖域算法。最小化R^n$中$x上的$Phi(X)=f(X)+h(c(X))$，其中f和c是光滑函数，h是多面体凸函数。这种形式的问题包括各种重要的应用，如极小极大优化，切比雪夫逼近，以及非线性规划中精确罚函数的最小化。该算法是对最近提出的求解非线性规划的逐次二次规划方法的改进，并利用对f和c的二阶逼近来避免Maratos效应。在适当的假设下，证明了该算法是全局二次收敛的。文中还给出了一些数值结果，证明了该算法的有效性。
This paper presents a trust region algorithm for solving the following problem. Minimize $phi (x) = f(x) + h(c(x))$ over $x in R^n $, where f and c are smooth functions and h is a polyhedral convex function. Problems of this form include various important applications such as min-max optimization, Chebyshev approximation, and minimization of exact penalty functions in nonlinear programming. The algorithm is an adaptation of a recently proposed successive quadratic programming method for nonlinear programming and makes use of the second-order approximations to both f and c in order to avoid the Maratos effect. It is proved under appropriate assumptions that the algorithm is globally and quadratically convergent to a solution of the problem. Some numerical results exhibiting the effectiveness of the algorithm are also reported.