求解一类非线性规划问题的新途径  

A new method for the solution of nonlinear programming problem

作　　者：朱国会[1] 沈渝路[2] 

机构地区：[1]重庆师范大学数学与计算机科学学院,重庆400047 [2]重庆通信学院基础部,重庆400035

出　　处：《长春工业大学学报》2004年第4期64-66,共3页Journal of Changchun University of Technology

基　　金：国家自然科学基金资助项目(10171118);重庆市教委基金资助项目(030809)

摘　　要：给出了一类约束函数单调而目标函数非单调的非线性规划问题的一种新的求解方法。首先给出了将其目标函数单调化的一种方法,然后,通过这个方法将这类非线性规划问题转化为等价的单调规划问题,进而利用已有的关于单调函数的凸化、凹化方法,可将其转化为等价的凹极小问题或反凸规划问题以及标准DC规划问题,再利用已有的关于这些规划问题求全局极小点的方法,可以求得原问题的全局极小点。A new method is applied to a kind of nonlinear programming problem with monotonic (restrictive) functions and non-monotonic objective functions. A method of monotonization of the (objective) function is first given, and then this kind of non-monotonic nonlinear programming probem can be converted into an equivalent monotonic programming problem via this newly presented (monotonization) method. By using the existing convexification and concavification methods, the (converted) monotonic programming problem can be converted into an equivalent concave minimization problem, or reverse convex programming problem, or canonic DC programming problem, and (consequently), the global minimizer of the original programming problem can be obtained by the (existing) methods.

关 键 词：单调化 非线性规划问题 全局极小点 

分 类 号：O221.2[理学—运筹学与控制论]