摘要
非线性方程组讨论的问题为F(x)=0,其中,F∶Rn→Rm.该问题广泛应用于工程、管理和经济学领域.非线性方程数值求解的典型方法之一是牛顿法.由于实际问题中存在大量的非光滑方程问题,近年来非光滑方程、特别是半光滑方程吸引了广大研究者的关注,半光滑牛顿法及其各类应用研究取得了丰硕的成果.本研究基于笔者近段的部分研究工作,介绍了非线性方程在无约束非光滑凸优化、约束最优化、非线性互补、变分不等式、最优控制、二阶段随机规划、随机线性互补和球面上的设计等八个方面的应用.
Nonlinear equations disusses the problem F（x） = 0,where F：R^n→R^m. Such problem arises from engineering, management and economy. The typical method for solving this problem is Newton method. Since there exist plenty of nonsmooth equation problems, the study of nonsmooth equations, especially for the so-called semismooth equations, attracts researcher＇s attention, and many good results are obtained from semismooth Newton method and applications. Based on our recent works, this paper introduces applications of nonlinear equations in eight aspects, which are unconstrained nonsmooth and convex optimization problems, constrained optimization problems, nonlinear complementarity, variational inequalities, optimal control problems, stochastic programming problems with two-stages, stochastic linear complementarity and design problems in ball.
出处
《长沙理工大学学报（自然科学版）》
CAS
2006年第4期1-7,共7页
Journal of Changsha University of Science and Technology:Natural Science
关键词
非线性方程
牛顿法
非光滑方程
nonlinear equations
Newton method
nonsmooth equations
