非光滑非凸约束优化问题的一种迫近束方法

A proximal bundle method for nonsmooth and nonconvex constrained optimization

束方法目前被公认为是解决非光滑优化问题的最有效、最有前景的方法之一,已经被成功应用到众多实际问题.利用次梯度局部测度将凸函数迫近束方法推广到非凸的约束优化问题并给出算法.该方法保证即使选取的初始点和迭代过程中的下降步不可行,所产生的序列仍会收敛到原问题的最优解.

Now Bundle methods are considered as one of the most efficient and promising methods for solving nonsmooth optimization problems.The methods have already been applied to many practical problems.In this paper,subgradient locality measures will be used to generalize the proximal bundle method of nonconvex constrained optimization.The algorithm will be presented,which will make sure that either the starting point or serious iterates are infeasible,the sequence will converge to the optimal solution.