一类求解全局优化问题的F-C函数法  

A Class of F-C Function Method for Solving Global Optimization Problem

作　　者：杨军君[1] 叶仲泉[1] 

机构地区：[1]重庆大学数理学院,重庆400030

出　　处：《计算机技术与发展》2009年第7期124-126,129,共4页Computer Technology and Development

摘　　要：填充函数法和跨越函数法是两种求解多变量、多极值函数全局最优化的有效方法,这些方法的关键是构造填充函数或者跨越函数。为此结合全局优化问题的填充函数法和跨越函数法,考虑优化问题minf(x)x∈Rn,针对f(x)为无Lipschitz连续函数,定义了一个求解全局优化问题的F-C函数。基于这个定义,提出了一类无参数的F-C函数。研究了所构造F-C函数的理论性质,并按照其理论性质提出了一个求解无约束优化问题的F-C函数算法。数值实验表明,所给的方法是有效的。The filled function method and cross function method are effective approaches for finding the global minima of multimodal and multidimensional functions, and the constructed filled function or cross function is vital to the results of optimization. In this paper, considering the optimization problem min f（x） x∈R^n,when f（x ） isn＇ t Lipschitz continuous function, propose a new definition of F- C function for solving global optimization, combined with filled function method and cross function method. Based on the definition, a class of parameter - free F- C function is proposed. Theoretical properties of the proposed F - C function are investigated, and an algorithm for global optimization problem is developed from the F - C function. Numerical experiments show that the method is effective.

关 键 词：全局优化 极小点 填充函数法 跨越函数法 F—C函数法 

分 类 号：O221.2[理学—运筹学与控制论] TP301.6[理学—数学]