对等式约束非线性规划问题的Hestenes-Powell增广拉格朗日函数的进一步研究(英文)  

Further Studies on the Hestenes-Powell Augmented Lagrangian Function for Equality Constraints in Nonlinear Programming Problems

作　　者：杜学武[1] 杨永建[2] 李铭明[3] 

机构地区：[1]大连理工大学应用数学系 [2]上海大学数学系,上海200444 [3]上海工程技术大学,上海201620

出　　处：《运筹学学报》2006年第1期38-46,共9页Operations Research Transactions

基　　金：Project supported by the Post-Doctoral Science Foundation of Dalian University of Technology and the Program for Excellent Young Teachers in Higher Institutions of Henan Province.

摘　　要：本文对用无约束极小化方法求解等式约束非线性规划问题的Hestenes-Powell 增广拉格朗日函数作了进一步研究．在适当的条件下,我们建立了Hestenes-Powell增广拉格朗日函数在原问题变量空间上的无约束极小与原约束问题的解之间的关系,并且也给出了Hestenes-Powell增广拉格朗日函数在原问题变量和乘子变量的积空间上的无约束极小与原约束问题的解之间的一个关系．因此,从理论的观点来看,原约束问题的解和对应的拉格朗日乘子值不仅可以用众所周知的乘子法求得,而且可以通过对Hestenes-Powell 增广拉格朗日函数在原问题变量和乘子变量的积空间上执行一个单一的无约束极小化来获得．In this paper, the Hestenes-Powell augmented Lagrangian function is again considered, for solving equality constrained problems via unconstrained minimization techniques. Under suitable assumptions, the relationship is established between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the space of problem variables and the solution of the original constrained problem, and a relationship is also presented between the unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers and the solution of the original constrained problem. Therefore, from the theoretical point of view, a solution of the constrained problem and the corresponding values of the Lagrange multipliers can be found not only by the well known method of multipliers but also by performing a single unconstrained minimization of the Hestenes-Powell augmented Lagrangian function on the product space of problem variables and multipliers.

关 键 词：运筹学 最优化 非线性规划 增广拉格朗日函数 Hestenes—Powell增广拉格朗日函数 

分 类 号：O316[理学—一般力学与力学基础] O221.2[理学—力学]