CONVEXIFICATION AND CONCAVIFICATION METHODS FOR SOME GLOBAL OPTIMIZATION PROBLEMS  

作　　者：WUZhiyou ZHANGLiansheng BAIFusheng YANGXinmin 

机构地区：[1]SchoolofMathematicsandComputerScience,ChongqingNormalUniversity,Chongqing400047 DepartmentofMathematics,ShanghaiUniversity,Shanghai200436,China [2]DepartmentofMathematics,ShanghaiUniversity,Shanghai200436,China [3]InstituteofMathematics,FudanUniversity,Shanghai200433,China [4]DepartmentofMathematicsandComputerScience,ChongqingNormalUniversity,Chongqing400047,China

出　　处：《Journal of Systems Science & Complexity》2004年第3期421-436,共16页系统科学与复杂性学报（英文版）

基　　金：This research is supported by the National Natural Science Foundation of China(Grant 10271073).

摘　　要：In this paper, firstly, we propose several convexification and concavification transformations to convert a strictly monotone function into a convex or concave function, then we propose several convexification and concavification transformations to convert a non-convex and non-concave objective function into a convex or concave function in the programming problems with convex or concave constraint functions, and propose several convexification and concavification transformations to convert a non-monotone objective function into a convex or concave function in some programming problems with strictly monotone constraint functions. Finally, we prove that the original programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem. Then the global optimal solution of the original problem can be obtained by solving the converted concave minimization problem, or reverse convex programming problem or canonical D.C. programming problem using the existing algorithms about them.

关 键 词：Global optimal solution concave minimization reverse convex programmingproblem D.C. programming problem CONVEXIFICATION CONCAVIFICATION 

分 类 号：TP311.1[自动化与计算机技术—计算机软件与理论] O174.13[自动化与计算机技术—计算机科学与技术]