A SIMPLICIAL HOMOTOPY ALGORITHM FOR COMPUTING ZERO POINTS ON POLYTOPES

作     者：陈开周 杨再福 梁正礼 

作者机构：Department of Applied Mathematics Xidian University Xi'an China 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：1994年第10卷第2期

页      面：186-193页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Zero point simplicial homotopy algorithm variable dimension algorithm,triangulation, polytope. 

摘      要：In this paper a triangulation of continuous and arbitrary refinement of grid sizes is proposed for simplicial homotopy algorithms to compute zero points on a polytope P. The proposed algorithm generates a piecewise linear path in P × [1,∞) from any chosen interior point x0 of P on level {1} to a solution of the underlying problem. The path is followed by making linear programming pivot steps in a linear system and replacement steps in the *** starting point x0 is left in a direction to one vertex of P. The direction in which x0 leaves depends on the function value at x0 and the polytope P. Moreover, we also give a new equivalent form of the Brouwer fixed point theorem on polytopes. This form has many important applications in mathematical programming and the theory of differential equations.