An ADMM algorithm for solving a proximal bound-constrained quadratic program

We will also be interested in solving a collection of such QPs that all have the same matrix A but different vectors b, v, l and u. It is possible to solve problem (1) in different ways, but we want to take advantage of the structure of our problem, namely the existence of the strongly convex µ term, and the fact that the N problems have the same matrix A. We describe here one algorithm that is very simple, has guaranteed convergence without line searches, and takes advantage of the structure of the problem. It is based on the alternating direction method of multipliers (ADMM), combined with a direct linear solver and caching the Cholesky factorization of A. Motivation Problem (1) arises within a step in the binary hashing algorithm of Carreira-Perpiñán and Raziperchikolaei (2015).