A Shadow Simplex Method for Infinite Linear Programs

A Shadow Simplex Method for Infinite Linear Programs

We present a Simplex-type algorithm, that is, an algorithm that moves from one extreme point of the infinite-dimensional feasible region to another not necessarily adjacent extreme point, for solving a class of linear programs with countably infinite variables and constraints. Each iteration of this method can be implemented in finite time, while the solution values converge to the optimal valu...

A Simplex Method for Infinite Linear Programs

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...

An asymptotic simplex method for singularly perturbed linear programs

Shadow Prices in Infinite-Dimensional Linear Programming

We consider the class of linear programs that can be formulated with infinitely many variables and constraints but where each constraint has only finitely many variables. This class includes virtually all infinite horizon planning problems modeled as infinite stage linear programs. Examples include infinite horizon production planning under time-varying demands and equipment replacement under t...

On gradient simplex methods for linear programs

A variety of pivot column selection rules based upon the gradient criteria (including the steepest edge) have been explored to improve the efficiency of the primal simplex method. Simplex-like algorithms have been proposed imbedding the gradient direction (GD) which includes all variables whose increase or decrease leads to an improvement in the objective function. Recently a frame work has bee...