ABSTRACT

In this paper, we first extend the diminishing stepsize method for nonconvex constrained problems presented in F. Facchinei, V. Kungurtsev, L. Lampariello and G. Scutari [Ghost penalties in nonconvex constrained optimization: Diminishing stepsizes and iteration complexity, To appear on Math. Oper. Res. 2020. Available at https://arxiv.org/abs/1709.03384.] to deal with equality constraints and a nonsmooth objective function of composite type. We then consider the particular case in which the constraints are convex and satisfy a standard constraint qualification and show that in this setting the algorithm can be considerably simplified, reducing the computational burden of each iteration.

摘要

在本文中，我们首先针对F. Facchinei，V。Kungurtsev，L.Lampariello和G. Scutari [非凸约束优化中的幽灵罚分：递减步长和迭代复杂度，在数学上出现。歌剧 Res。2020年。可在https://arxiv.org/abs/1709.03384。]处理等式约束和复合类型的不平滑目标函数。然后，我们考虑约束为凸且满足标准约束条件的特殊情况，并表明在这种设置下，可以大大简化算法，从而减少每次迭代的计算负担。