Bregman primal–dual first-order method and application to sparse semidefinite programming

Abstract We present a new variant of the Chambolle–Pock primal–dual algorithm with Bregman distances, analyze its convergence, and apply it to centering problem in sparse semidefinite programming. The novelty method is line search procedure for selecting suitable step sizes. obviates need estimating norm constraint matrix strong convexity constant kernel. As an application, we discuss large-scale programming coefficient matrices. logarithmic barrier function cone positive completable matrices used as distance-generating For this distance, complexity evaluating proximal operator shown be roughly proportional cost Cholesky factorization. This much cheaper than standard Euclidean which requires eigenvalue decomposition.