非凸域上函数极小化问题的组合同伦方法  

Combined homotopy methods of the function minimization problems over nonconvex region

作　　者：刘庆怀[1] 

机构地区：[1]长春工业大学应用数学研究所,吉林长春130012

出　　处：《长春工业大学学报》2012年第5期605-610,共6页Journal of Changchun University of Technology

基　　金：国家自然科学基金资助项目(1771020);吉林省自然科学基金资助项目(20101597)

摘　　要：对非凸域上函数极小化问题的同伦方法进行了讨论。首先,简述了其发展历程;其次,介绍了用组合同伦算法求解此类问题的有关非凸可行域的若干边界限制条件,重点阐述法锥条件和广义法锥条件,诸如弱法锥条件、拟法锥条件与伪锥条件等;最后,给出在这些边界条件下求解非凸规划问题的各类组合同伦方程。In this paper, homotopy methods of the function minimization problems are considered over non-convex region. First, we go over the development history of combined homotopy method. Secondly, some restricted conditions of the non-convex feasible region are introduced for solving the nonlinear programming with homotopy method, such as weak normal cone condition, quasi-normal cone condition and pseudo cone condition, and so on. Especially, we elaborate normal cone condition and general normal cone condition. At last, under these boundary conditions we give the corresponding homotopy equations.

关 键 词：同伦方法 非凸规划 内点算法 整体算法 

分 类 号：O221.2[理学—运筹学与控制论]