In this paper we develop a long-step primal-dual infeasible path-following algorithm for convex quadratic programming (CQP) whose search directions are computed by means of a preconditioned iterative linear solver. We propose a new linear system, which we refer to as the augmented normal equation (ANE), to determine the primal-dual search directions. Since the condition number of the ANE coeffi...

Quantified Boolean Formulas (QBF) provide a good language for modeling many complex questions about deterministic systems, especially questions involving control of such systems and optimizing choices. However, translators typically have one set way to encode the description of a system and a property, or question about the system, often without distinguishing between the two. In many cases the...

We suggest new dual algorithms and iterative methods for solving monotone generalized variational inequalities. Instead of working on the primal space, this method performs a dual step on the dual space by using the dual gap function. Under the suitable conditions, we prove the convergence of the proposed algorithms and estimate their complexity to reach an ε-solution. Some preliminary computat...

We show that if there exists a strongly polynomial time algorithm that nds a basis which is optimal for both the primal and the dual problems given an optimal solution for one of the problems then there exists a strongly polyno mial algorithm for the general linear programming problem On other hand we give a strongly polynomial time algorithm that nds such a basis given any pair of optimal solu...

In this paper we propose a perturbed proximal primal dual algorithm (PProx-PDA) for an important class of optimization problems whose objective is the sum of smooth (possibly nonconvex) and convex (possibly nonsmooth) functions subject to a linear equality constraint. This family of problems has applications in a number of statistical and engineering applications, for example in high-dimensiona...

The dual Phase-I algorithm using the most-obtuse-angle row pivot rule is very efficient for providing a dual feasible basis, in either the classical or the basisdeficiency-allowing context. In this paper, we establish a basis-deficiency-allowing Phase-I algorithm using the so-called most-obtuse-angle column pivot rule to produce a primal (deficient or full) basis. Our computational experiments ...

The dual simplex algorithm is an attractive alternative as a solution method for linear programming problems. Since the addition of new constraints to a problem typically breaks primal feasibility but not dual feasibility, the dual simplex can be deployed for rapid reoptimization, without the need of finding new primal basic feasible solutions. This is especially useful in integer programming, ...

We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm, and then transforming it into a primal-dual algorithm. This was done in the case of the 2-approximation algorithms for the f...

We present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dial grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points xi. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that sp...

Primal-dual algorithms, which are proposed to solve reformulated convex-concave saddle point problems, have been proven to be effective for solving a generic class of convex optimization problems, especially when the problems are ill-conditioned. However, the saddle point problem still lacks a distributed optimization framework where primal-dual algorithms can be employed. In this paper, we pro...