In this paper, we present a simplex method for linear programs in standard form, or more precisely, linear optimization problems that have countably many non-negative variables and countably many equality constraints. Important special cases of these problems include infinite horizon deterministic dynamic programming problems and network flow problems with countably infinite nodes and arcs. Aft...

This paper introduces the design and implementation of two parallel dual simplex solvers for general large scale sparse linear programming problems. One approach, called PAMI, extends a relatively unknown pivoting strategy called suboptimization and exploits parallelism across multiple iterations. The other, called SIP, exploits purely single iteration parallelism by overlapping computational c...

• By convention, the vector formed by taking together all the basic variables is denoted xB. Similarly, cB, `B and uB are formed by taking together the same indices of c, ` and u, respectively. The same notation is also used for the indices in L and U , giving cL, cU , `L, `U , uL, and uU . We already defined B as taking together the basic columns of A. The remaining (nonbasic) columns form the...

High dimensional sparse learning has imposed a great computational challenge to large scale data analysis. In this paper, we are interested in a broad class of sparse learning approaches formulated as linear programs parametrized by a regularization factor, and solve them by the parametric simplex method (PSM). Our parametric simplex method offers significant advantages over other competing met...