基于统计模型的一维全局最优解
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| 摘 要 本文综述了基于全局优化方法的统计多通道功能模型。这个理论和方法等方面加以了强调。 关键字：最优化;统计模型;收敛 1. 简介 全局最优化对于应用是一个最重要的科目，同时在最优化中是最难的科目之一,甚至在一般计算的中也是一个很难的科目。由于实用的重要性这一领域和缺乏数学理论（与局部优化理论相比），许多不同应用科目的专家提出了不同的启发式方法。(毕业设计) 数学研究领域中开始使用一种标准计算方法：一类问题的定义是指通过目标函数的基本条件和方法的收敛性的进行研究。一类利普希茨函数和已知的利普希茨常量是最受欢迎的一类函数。例如，用特殊的方法研究最小凹函数和二次函数。虽然在很多文章中，它不是着重强调极小极大方法的使用。根据不乐观的结果意味着采用指数复杂算法，因些研究优化算法变得很重要。然而，它证明了优化算法也有指数的复杂性。极小极大方法无法脱离指数复杂性，因为广泛的一类多式函数包含病理例子。此外，人们清楚地看到，在极小限定下改造是没有用的。 第一篇论文在全局优化方法的是通过参数的平均值的合理来证明 ，然而，使用H.Kushner模型的延伸很难达到多层面。该模型在许多真正的优化问题中也似乎是不合适的，因为样本函数的可微性. 方法的延伸给光滑函数模型通过计算困难也给予阻止。因此，一个基于统计模型的全局优化方法的发展上从一开始就似乎难以从理论上以及从算法的实施的角度上看。 Abstract This paper presents a review of global optimization methods based on statistical models of multimodal functions. The theoretical and methodological aspects are emphasized. Keywords: Optimization, statistical models, convergence 1. Introduction Global optimization is one of the most important subjects for applications and at the same time one of the most difficult subjects in optimization and even computing in general. Because of the practical importance of the field and the shortage of mathematical theory (compared with local optimization theory),many heuristic methods were proposed by the experts of different applied subjects. Mathematical investigation in the field began using a standard approach of computing: a class of problems is defined by means of postulating features of an objective function and convergence of a method is investigated. A class of Lipshitz functions with known Lipshitz constant is the most popular class of functions. Special methods were investigated for minimization of concave and quadratic functions, for example. Although in many papers it is not formally emphasized, the minimax approach was used. In light of pessimistic results implying exponential complexity of the proposed algorithms, investigation of optimal algorithms became important. However, it was proved that optimal algorithms also have exponential complexity. The minimax approach can not escape exponential complexity because a broad class of multimodal functions contains pathological examples. Moreover, it became clear that in the minimax setting adaptation can not help. 全文 14000字 |