直接最优化方法的收敛性与不动点

最优化方法中的直接法是仅仅利用目标函数值(或者通过试验结果)的信息,试图去寻求最优解.直接法迭代步骤简单,特别当目标函数的解析表达式十分复杂,甚至写不出来时,那些要求计算目标函数的偏导数的方法(称为解析方法)就无能为力了.然而,多因

THE CONVERGENCE AND FIXED POINT ABOUT DIRECT SEARCH METHOD

In this paper,we give a necessary and sufficient condition under which the fixedpoint of the axial iterative method is an optimal soliution.From the uniform pointof view about the fixed point we present that the limit point of sequences generatedfrom six methods (powell's,axial iterative,a variant of the axial iterative,reducingdimensionality,Hooke-Jeeves',Rosenbrock's) are fixed points of the axial itertivomethod.Hence the convergences of these six methods are proved,and the necessaryand sufficient conditions of convergences of these six methods are obtained.From thepoint of view of the fixed point we also prove the convergences of the simplexsearch method and the rectangular evolutionary method,and obtain necessary andsufficient conditions of the convergences.