The primal-dual method (or primal-dual schema) is another means of solving linear programs. The basic idea of this method is to start from a feasible solution y to the dual program, then attempt to find a feasible solution x to the primal program that satisfies the complementary slackness conditions. If such an x cannot be found, it turns out that we can find a better y in terms of its objectiv...

This paper describes several methods for solving nonlinear complementarity problems. A general duality framework for pairs of monotone operators is developed and then applied to the monotone complementarity problem, obtaining primal, dual, and primal-dual formulations. We derive Bregman-function-based generalized proximal algorithms for each of these formulations, generating three classes of co...

We develop a primal dual active set with continuation algorithm for solving the l-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it first identifies the active set from both primal and dual variables, and then updates...

We view the optimal single commodity network flow problem with linear arc costs and its dual as a pair of monotropic programming problems, i.e. problems of minimizing the separable sum of scalar extended real-valued convex functions over a subspace. For such problems directions of cost improvement can be selected from among a finite set of directions--the elementary vectors of the constraint su...