A Shadow Simplex Method for Infinite Linear Programs

Authors:
Archis Ghate;Dushyant Sharma;Robert L. Smith
Affiliations:
Industrial and Systems Engineering Department, University of Washington, Seattle, Washington 98195;Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109;Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109
Venue:
Operations Research
Year:
2010

Citing 24
Cited 0

Infinite horizon stochastic programs

SIAM Journal on Control and Optimization
A new optimality criterion for nonhomogeneous Markov decision processes

Operations Research
Infinite horizon optimization

Mathematics of Operations Research
Duality in infinite dimensional linear programming

Mathematical Programming: Series A and B
An algorithm for a class of continuous linear programs

SIAM Journal on Control and Optimization
Decision roll and horizon roll processes in infinite horizon discounted Markov decision processes

Management Science
Constrained discounted dynamic programming

Mathematics of Operations Research
Shadow Prices in Infinite-Dimensional Linear Programming

Mathematics of Operations Research
Approximating Extreme Points of Infinite Dimensional Convex Sets

Mathematics of Operations Research
Optimization by Vector Space Methods

Optimization by Vector Space Methods
Markov Decision Processes: Discrete Stochastic Dynamic Programming

Markov Decision Processes: Discrete Stochastic Dynamic Programming
Introduction to Stochastic Dynamic Programming: Probability and Mathematical

Introduction to Stochastic Dynamic Programming: Probability and Mathematical
Simplex-Like Trajectories on Quasi-Polyhedral Sets

Mathematics of Operations Research
Introduction to Linear Optimization

Introduction to Linear Optimization
Approximation Schemes for Infinite Linear Programs

SIAM Journal on Optimization
Convergence of a General Class of Algorithms for Separated Continuous Linear Programs

SIAM Journal on Optimization
Duality and Existence of Optimal Policies in Generalized Joint Replenishment

Mathematics of Operations Research
Online searching with turn cost

Theoretical Computer Science - Approximation and online algorithms
Extreme point characterizations for infinite network flow problems

Networks
Solution and Forecast Horizons for Infinite-Horizon Nonhomogeneous Markov Decision Processes

Mathematics of Operations Research
A simplex based algorithm to solve separated continuous linear programs

Mathematical Programming: Series A and B
A simplex algorithm for minimum-cost network-flow problems in infinite networks

Networks
An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces

Mathematics of Operations Research
Characterizing extreme points as basic feasible solutions in infinite linear programs

Operations Research Letters

Quantified Score

Hi-index	0.00

Visualization

Abstract

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, whereas the solution values converge to the optimal value as the number of iterations increases. This simplex-type algorithm moves to an adjacent extreme point and hence reduces to a true infinite-dimensional simplex method for the important special cases of nonstationary infinite-horizon deterministic and stochastic dynamic programs.