Developing Lagrangian-based Methods for Nonsmooth Nonconvex Optimization

arXiv:2404.09438v1 Announce Type: cross
Abstract: In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified framework for developing Lagrangian-based methods, which takes a single-step update to the primal variables by some subgradient methods in each iteration. These subgradient methods are ``embedded'' into our framework, in the sense that they are incorporated as black-box updates to the …

abstract arxiv constraints cs.lg framework function math.oc optimization paper primal stat.ml type update variables