Dynamic programming and inequalities

Approximate Dynamic Programming via Iterated Bellman Inequalities

In this paper we introduce new methods for finding functions that lower bound the value function of a stochastic control problem, using an iterated form of the Bellman inequality. Our method is based on solving linear or semidefinite programs, and produces both a bound on the optimal objective, as well as a suboptimal policy that appears to works very well. These results extend and improve boun...

Dynamic-Programming-Based Inequalities for the Unbounded Integer Knapsack Problem

We propose a new hybrid approach to solve the unbounded integer knapsack problem (UKP), where valid inequalities are generated based on intermediate solutions of an equivalent forward dynamic programming formulation. These inequalities help tighten the initial LP relaxation of the UKP, and therefore improve the overall computational efficiency. We also extended this approach to solve the multi-...

Dynamic Programming and Dynamic Games

Modern Computational Applications of Dynamic Programming

Computational dynamic programming, while of some use for situations typically encountered in industrial and systems engineering, has proved to be of much greater significance in many areas of computer science. We review some of these applications here.

Bilevel Programming and Maximally Violated Valid Inequalities

In recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MIPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MIPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generat...