直接搜索法历史和现状

Direct search methods:then and now

直接搜索法：历史和现状

Robert Michael Lewis1,a,Virginia Torezon2,*,,b a,Michael W. Trosset a c,

a ICASE, Mail Stop 132C, NASA Langley Research Center, Hampton,V A 23681-2199. USA

b Department of Computer Science, College of William & Mary, P.O. Box 8795, Williamsburg, V A 23187-8795, USA

c Department of Mathematics, College of William & Mary, P.O. Box 8795, Williamsburg, V A 23187-8795, USA

Received 1 July 1999; received in revised form 23 February 2000 Abstract

摘要

我们讨论无约束优化的直接搜索法。我们从现在的观点来看这类与导数无关的算法，

主要集中在1960到1971年的直接搜索法发展的黄金时期。我们首先讨论在未构建目标模型的情况怎样使用直接搜索法。然后我们考虑一些经典直接搜索法并揭示那些年这类算法的进展。特别地，当原始直接搜索法开始直接利用启发式方法时，更多近来的分析表明，虽然不是全部但大部分启发式方法实际上已经足可以保证迭代序列中至少有一个子序列全局收敛到目标函数的一阶驻点。

关键词：求导无关优化；直接搜索法；模式搜索法

We discuss direct search methods for unconstrained optimization. We give a modern

perspective on this classical family of derivative-free algorithms, focusing on the development of direct search methods during their golden age from 1960 to 1971. We discuss how direct search methods are characterized by the absence of the construction of a model of the objective. We then consider a number of the classical direct search methods and discuss what research in the intervening years has uncovered about these algorithms. In particular, while the original direct search methods were consciously based on straightforward heuristics, more recent analysis has shown that in most – but not all – cases these heuristics actually suffice to ensure global convergence of at least one subsequence of the sequence of iterates to a first-order stationary point of the objective function. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Derivative-free optimization; Direct search methods; Pattern search methods

1.Introduction

1．引言

罗伯特·胡克和T.A.捷吾斯首先在1961年的计算机械协会期刊上的一篇论文上提出“直接搜索”[12].在他们的论文的引言中这样描述直接搜索：

Robert Hooke and T.A. Jeeves coined the phrase “direct search” in a paper that appeared in 1961 in the journal of the Association of Computing Machinery [12]. They Provided the following description of direct search in the introduction to their paper:

*Corresponding author.

E-mail addressed: bucharoo@ (R.M. Lewis), va@ (V. Torczon), trosset@ (M.W. Trosset).

1This research was supported by the National Aeronautics and Space Administration under NASA Contract No.NAS1-97046.

2This research was supported By the National Science Foundation under Grant CCR-9734044 and by the National Aeronautics and Space Administration under NASA Contract No. NASI-97046, while the author was in residence at the Institute for Computer Applications in Science and Engineering (ICASE).

0377-0427/00/$-see front matter © 2000 Elsevier Science B.V. All rights reserved.

Pll:S0377-0427(00)00423-4

我们用“直接搜索”术语来描述试验解的有序检查，包括每个试验解与当前“最好”解的比较和决定（作为以前结果的函数）下一个试验解的策略。该术语暗示我们的优先选择是基于经验的。对于直接搜索策略，一般的经典分析方法起不到任何作用。

We use the phrase “direct search” to describe sequential examination of trial solutions involving comparison of each trial solution with the “best”obtained up to that time together with a strategy for determining (as a function of earlier results) what the next trial solution will be. The phrase