A filter proximal bundle algorithm is presented for nonsmooth nonconvex constrained optimization problems. The new algorithm is based on the proximal bundle method and utilizes the improvement function to regularize the constraint. At every iteration by solving a convex piecewise-linear subproblem a trial point is obtained. The process of the filter technique is employed either to accept the trial point as a serious iterate or to reject it as a null iterate. Under some mild and standard assumptions and for every possible choice of a starting point, it is shown that every accumulation point of the sequence of serious iterates is feasible. In addition, there exists at least one accumulation point which is stationary for the improvement function. Finally, some encouraging numerical results show that the proposed algorithm is effective.

针对非光滑非凸约束优化问题，提出了一种滤波器近端束算法。新算法基于近端束方法，并利用改进函数对约束进行正则化。在每次迭代中，通过求解凸分段线性子问题，可以获得一个试验点。采用过滤技术的过程要么接受试验点为严重迭代，要么拒绝试验点为无效迭代。在一些温和和标准的假设下，对于起点的每个可能选择，都表明严重迭代序列的每个累加点都是可行的。另外，存在至少一个固定点用于提高功能。最后，一些令人鼓舞的数值结果表明该算法是有效的。