Abstract: We will demonstrate a wide range of first-order optimization methods that can

be built from a few concepts and tricks in the monotone operator theory. They

include gradient, proximal-gradient, (proximal) method of multipliers, alternating

minimization, PDHG, Chambolle Pock, Condat-Vu, (standard, proximal, and

linearized) ADMM, and PD3O. Finite-sum and block-coordinate-friendly properties

are used to develop parallel and asynchronous methods. However, we will

leave out topics such as line search, Nesterov/heavy-ball accelerations, conditional

gradients, and second-order methods. We will also discuss how to recognize

unbounded, infeasible, and other pathological problems by first-order methods.

Co-author: Ernest K. Ryu and Yanli LI.

BIO:  Wotao Yin

Affiliation: University of California; Los Angeles