A UNIFIED APPROACH TO THE IMPLEMENTATION OF SEVERAL RESTART FIXED-POINT ALGORITHMS AND A NEW VARIABLE DIMENSION ALGORITHM

作     者：KOJIMA, M YAMAMOTO, Y 

作者机构：UNIV TSUKUBAINST SOCIOECON PLANNINGSAKURAIBARAKI 305JAPAN 

出 版 物：《MATHEMATICAL PROGRAMMING》 (数学规划)

年 卷 期：1984年第28卷第3期

页      面：288-328页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 

主　　题：Fixed Point Algorithms Systems of Nonlinear Equations Variable Dimension Algorithms Piecewise Smooth Mappings Piecewise Linear Mappings Complementary Pivoting 

摘      要：We present a unified description of a class of restart fixed point algorithms including Merrill s method and several variable dimension algorithms for their implementation on computers. Based on this description we show that some pivot-saving techniques originally developed for the homotopy methods can be applied to the class. We also propose a new variable dimension algorithm having 3n-1 rays along which we can move toward a solution. Some numerical comparisons of the simplicial restart algorithms, Merrill s method, the 2n-method, the octahedral method and the new one, support that the latter two methods are more efficient than the others.