Fixing and extending some recent results on the ADMM algorithm

We first point out several flaws in the recent paper {\it [R. Shefi, M. Teboulle: Rate of convergence analysis of decomposition methods based on the proximal method of multipliers for convex minimization, SIAM J. Optim. 24, 269–297, 2014]} that proposes two ADMM-type algorithms for solving convex optimization problems involving compositions with linear operators and show … Read more

A general double-proximal gradient algorithm for d.c. programming

The possibilities of exploiting the special structure of d.c. programs, which consist of optimizing the difference of convex functions, are currently more or less limited to variants of the DCA proposed by Pham Dinh Tao and Le Thi Hoai An in 1997. These assume that either the convex or the concave part, or both, are … Read more

A forward-backward-forward differential equation and its asymptotic properties

In this paper, we approach the problem of finding the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space via an implicit forward-backward-forward dynamical system with nonconstant relaxation parameters and stepsizes of the resolvents. Besides proving existence and uniqueness of strong global solutions … Read more