基于经典的增广拉格朗日乘子法, 对求解一类带有特定结构（主要是针对凸规划）的非光滑等式约束优化问题, 我们提出、分析并测试了一个新算法. 在极小化增广拉格朗日函数的每一步迭代中, 该算法有效结合了带有非单调线性搜索的交替方向技术, 我们建立了算法的收敛性, 并用它来求解在带有全变差正则化的图像恢复问题.-Based on the classic augmented Lagrangian multiplier method, we propose, analyze and test an algorithm for solving a class of equality-constrained nonsmooth optimization problems (chiefly but not necessarily convex programs) with

a particular structure. The algorithm effectively combines an alternating direction

technique with a nonmonotone line search to minimize the augmented Lagrangian

function at each iteration. We establish convergence for this algorithm, and apply it

to solving problems in image reconstruction with total variation regularization.