A Composed Alternating Relaxed Projection Algorithm for Convex Feasibility Problems

ADMM and Linearized ADMM for Weakly Convex Minimization

We study a class of weakly convex optimization problems in which the objective is the sum of a smooth convex term and a weakly convex term that may be nonsmooth. To exploit this structure, we develop a splitting technique based on the alternating direction method of multipliers (ADMM), which decouples the minimization...

Subspace methods for min-max problems

This paper introduces four groups of subspace methods for nonlinear monotone equations, with applications to large-scale machine learning problems. The methods use Jacobian-free subspace ({\tt JFS}) directions of conjugate-gradient type, combined with either fixed step sizes or variable step sizes generated by the proj...

Convergence Rates of Subgradient Algorithms for Convex Feasibility Problems

Derivative-Free Spectral Projection Methods for Large-Scale Monotone Equations

We introduce two derivative-free spectral projection methods for large-scale monotone equations with convex constraints. The first, SOPP (Spectral Optimal-Perry Projection), selects its Perry parameter by minimizing the condition number of a symmetrized Perry matrix over its positive definite range, in place of the eig...

Projected Subgradient Methods for a Class of Nonsmooth and Nonconvex Optimization Problems

We investigate the optimization problem of minimizing a nonsmooth function that satisfies a nonsmooth version of the descent lemma over a nonempty and closed but not necessarily convex set. The objective function belongs to the class of upper-$\mathcal{C}^2$ functions, whereas the constraints may promote a sparse or lo...

Envelopt: Constrained Convex Composite Optimization

We introduce Envelopt, a globally convergent iterative framework for a broad class of structured optimization problems where a smooth objective is augmented by a nonsmooth convex regularizer composed with a smooth mapping, and the variables are subject to general smooth constraints. All smooth functions may be nonconve...