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...

An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described It applies sequential quadratic programming techniques to a sequence of barrier problems and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives This framework permits primal and primal dual steps but the paper focuses on the ...

We present pure-integer Gomory cuts in a way so that they are derived with respect to a “dual form” pure-integer optimization problem and applied on the standard-form primal side as columns, using the primal simplex algorithm. The input integer problem is not in standard form, and so the cuts are derived a bit differently. In this manner, we obtain a finitely-terminating version of pure-integer...