Analysis of generalized pattern searches
Analysis of generalized pattern searches
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DOI：
10.1137/s1052623400378742
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发表时间：
2003-01-01
影响因子：
3.1
通讯作者：
Dennis, JE
中科院分区：
文献类型：
--
作者：
Audet, C;Dennis, JE
本文对求解无约束和线性约束优化问题的刘易斯和Torczon广义模式搜索（GPS）类方法进行了一个新的收敛性分析。这种分析的动机是希望了解算法在许多实际问题满足的假设下的成功行为。具体地说，即使目标函数是不连续的或扩展值的，该方法找到一个极限点与一些最小化的性质。简单的例子表明，在极限点的最优性条件的强度不仅取决于算法，而且还取决于它使用的方向和目标在极限点的光滑性。本文的贡献是提供一个简单的收敛性分析，提供详细的最优性条件的关系，客观的光滑性和方向的算法，它给出了以前的结果作为推论。
This paper contains a new convergence analysis for the Lewis and Torczon generalized pattern search (GPS) class of methods for unconstrained and linearly constrained optimization. This analysis is motivated by a desire to understand the successful behavior of the algorithm under hypotheses that are satisfied by many practical problems. Specifically, even if the objective function is discontinuous or extended-valued, the methods find a limit point with some minimizing properties. Simple examples show that the strength of the optimality conditions at a limit point depends not only on the algorithm, but also on the directions it uses and on the smoothness of the objective at the limit point in question. The contribution of this paper is to provide a simple convergence analysis that supplies detail about the relation of optimality conditions to objective smoothness properties and to the de ning directions for the algorithm, and it gives previous results as corollaries.