非光滑约束问题的既约次梯度法

１引言 对带约束的不可微的非线性规划问题，由于不能使用梯度，求极小点就比较困难．本文给出解决此问题的一种有效的算法． ２　非光滑约束问题的既约次梯度法 １）非线性规划问题的Ｌａｅｒａｎｅ对偶理论 考虑下面非线性规划问题其中ｇ（ｘ）＝（ｇ１（ｘ），…，ｇｒ（ｘ））Ｔ，ｈ（ｘ））＝（ｈ１（ｘ），…，ｈｍ（ｘ））Ｔ，ｆ（ｘ）＝　　　　　　Ｒｎ中是Ｌｉｓｐｓｃｈｉｔｚ连续的ｉ＝１，２，…，ｒ，ｊ＝１，２，…，ｍ相应的Ｌａｇｒａｎｇｅ对偶问题为其中　　（ｕ，　）＝ｉｎｆＬ（ｘ；ｕ，ｖ）＝ｉｎｆ（ｆ（ｘ）＋ｕＴ…

AN AGGREGATE SUBGRADIENT METHODS FOR NONSMOOTH CONSTRAINED MINIMIZATION

In this paper, by the Lagrange dual theory, the nonsmooth constrained minimization, where the objective function and the constrained functions are Lips- chitzian, can be regarded as a convex programming with linear constrains. We give the related aggregate subgradient method, and prove that either a solution of this nonsmooth constrained minimization problem can be obtained after a finite number of iterations or a sequence {xk} is generated so that each cluster point of {xk} is an optimal solution of the problem. The numerical examples show that the new method suggested here is practical and efficient.