Derivative-free optimization methods for finite minimax problems
Derivative-free optimization methods for finite minimax problems
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DOI：
10.1080/10556788.2011.638923
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发表时间：
2013-04
影响因子：
2.2
通讯作者：
W. Hare;M. S. Macklem
中科院分区：
文献类型：
--
作者：
W. Hare;M. S. Macklem
无导数优化专注于设计方法来解决优化问题，而无需函数的分析知识。本文考虑有限极大极小问题minxmaxi =1，2，.，Nfi（x）的无导数方法的设计问题.为了有效地解决问题，我们试图利用光滑的子结构的问题。使用Burke等人[J. V. Burke，A.S.刘易斯和M.L.奥弗顿，近似次微分的随机抽样梯度，数学。第27（3）（2002）号决议，pp. 567-584; J.V. Burke，A.S.刘易斯和M.L. Overton，一种用于非光滑非凸优化的鲁棒梯度采样算法，SIAM J. Optim. 15（3）（2005），pp. 751-779（电子）]，我们创建了一个强大的单纯形梯度下降方向的想法，并使用它来加速收敛。收敛性证明表明，所得到的算法适合定向直接搜索框架。数值试验表明了算法对有限极大极小问题的有效性。
Derivative-free optimization focuses on designing methods to solve optimization problems without the analytical knowledge of the function. In this paper, we consider the problem of designing derivative-free methods for finite minimax problems: min x max i=1, 2, …, N f i (x). In order to solve the problem efficiently, we seek to exploit the smooth substructure within the problem. Using ideas developed by Burke et al. [J.V. Burke, A.S. Lewis, and M.L. Overton, Approximating subdifferentials by random sampling of gradients, Math. Oper. Res. 27(3) (2002), pp. 567–584; J.V. Burke, A.S. Lewis, and M.L. Overton, A robust gradient sampling algorithm for nonsmooth, nonconvex optimization, SIAM J. Optim. 15(3) (2005), pp. 751–779 (electronic)], we create the idea of a robust simplex gradient descent direction and use it to accelerate convergence. Convergence is proven by showing that the resulting algorithm fits into the directional direct-search framework. Numerical tests demonstrate the algorithm's effectiveness on finite minimax problems.