运筹学学报
運籌學學報
운주학학보
OR TRANSACTIONS
2007年
1期
73-84
,共12页
运筹学%对偶间隙%Lagrangian函数%收敛性%最优路径
運籌學%對偶間隙%Lagrangian函數%收斂性%最優路徑
운주학%대우간극%Lagrangian함수%수렴성%최우로경
Operations research%duality gap%Lagrangian function%convergence%optimal path
针对一般的非线性规划问题,利用某些Lagrange型函数给出了一类Lagrangian对偶问题的一般模型,并证明它与原问题之间存在零对偶间隙.针对具体的一类增广Lagrangian对偶问题以及几类由非线性卷积函数构成的Lagrangian对偶问题,详细讨论了零对偶间隙的存在性.进一步,讨论了在最优路径存在的前提下,最优路径的收敛性质.
針對一般的非線性規劃問題,利用某些Lagrange型函數給齣瞭一類Lagrangian對偶問題的一般模型,併證明它與原問題之間存在零對偶間隙.針對具體的一類增廣Lagrangian對偶問題以及幾類由非線性捲積函數構成的Lagrangian對偶問題,詳細討論瞭零對偶間隙的存在性.進一步,討論瞭在最優路徑存在的前提下,最優路徑的收斂性質.
침대일반적비선성규화문제,이용모사Lagrange형함수급출료일류Lagrangian대우문제적일반모형,병증명타여원문제지간존재령대우간극.침대구체적일류증엄Lagrangian대우문제이급궤류유비선성권적함수구성적Lagrangian대우문제,상세토론료령대우간극적존재성.진일보,토론료재최우로경존재적전제하,최우로경적수렴성질.
In this paper, we propose a general model of a class of Lagrangian dual problem for the general nonlinear programming problem with respect to some Lagrangetype functions. We obtain that the zero duality gap exists between this class of Lagrangian dual problem and the primal problem. We discuss detailedly the existence of the zero duality gap for a class of augmented Lagrangian problem, and several classes of nonlinear convolution Lagrangian dual problems. Finally, we discuss the convergence of optimal path.
