摘要
研究有不等式约束的非线性规划问题,构造了一种新的两阶段算法:(1)利用传统优化方法求出原问题的一个局部极小点x*;(2)基于当前局部极小点和"准"罚函数的思想构造了一个辅助函数,该辅助函数连续可微、有界并且是凸的,该函数的局部极小点y*很容易求得,并且y*位于比x*更低的盆域中,从而y*可以作为第一阶段中的初始点,从而找到另一个更好的局部极小点.两个阶段不断循环,只要原问题具有有限个局部极小点,就可以找到它的全局极小点.为了测试算法的性能,对几个测试问题进行了求解.结果表明算法有效的,可以快捷的跳出局部极小点达到全局极小点.
The global optimization problem with inequality constraints is considered in this paper.A novel algorithm is proposed which consists of the tw o phases：（1） A local minimizer x＊ of the original function is found by a traditional method.（2） An auxiliary function is constructed by using a smoothing penalty function at the current local minimizer first.This function is continuously differentiable,bounded below and convex,thus its optimal solution can be easily found w ithout numerical overflow and unstableness.Then a local minimizer y＊ of this function is found w hich w ill be no w orse than current local minimizer x＊ of the original function,i.e.,y＊ w ill locate at a low er basin of the original function than the basin x＊ locates.Thus y＊ can be used as an initial point of the minimization of the original function at the first phase to further search for a better local minimizer.These tw o phases are repeated and the local minimizers found at the first phase for the original function w ill be better and better.Finally the global optimal solution can be found if there are a finite number of local minimizers.In order to test the performance of the proposed algorithm,the computer simulations on several test problems are made and the results indicate the proposed algorithm is efficient,effective,and can escape quickly from local minimizers to find the global minimizer.
出处
《小型微型计算机系统》
CSCD
北大核心
2013年第7期1672-1674,共3页
Journal of Chinese Computer Systems
基金
国家自然科学基金项目(61272119
11226173)资助
关键词
辅助函数法
全局优化
约束非线性规划问题
auxiliary function method
global optimization
constrained nonlinear optimization problem
