We present a computational approach to the saddle-point formulation for the Nash equilibria of two-person, zero-sum sequential games of imperfect information. The algorithm is a first-order gradient method based on modern smoothing techniques for non-smooth convex optimization. The algorithm requires O(1//) iterations to compute an-equilibrium, and the work… (More)
We develop first-order smoothing techniques for saddle-point problems that arise in finding a Nash equilibrium of sequential games. The crux of our work is a construction of suitable prox-functions for a certain class of polytopes that encode the sequential nature of the game. We also introduce heuristics that significantly speed up the algorithm, and… (More)
Fixed-width MDDs were introduced recently as a more refined alternative for the domain store to represent partial solutions to CSPs. In this work, we present a systematic approach to MDD-based constraint programming. First, we introduce a generic scheme for constraint propagation in MDDs. We show that all previously known propagation algorithms for MDDs can… (More)
We propose a new gradient based scheme to approximate Nash equilibria of large sequential two-player, zero-sum games. The algorithm uses modern smoothing techniques for saddle-point problems tailored specifically for the polytopes used in the Nash equilibrium problem.
Liquefied Natural Gas (LNG) is steadily becoming a common mode for commercializing natural gas. In this paper, we develop methods for improving both lower and upper bounds for a previously stated form of an LNG inventory routing problem. A Dantzig-Wolfe-based decomposition approach is developed for LNG inventory routing problem (LNG-IRP) attempting to… (More)
We study the problem of finding optimal space-time trajectories for two factory cranes or hoists that move along a single overhead track. Each crane is a assigned a sequence of pickups and deliveries at specified locations that must be performed within given time windows. The cranes must be operated so as not to interfere with each other, although one crane… (More)
We describe a heuristic algorithm for scheduling the movement of multiple factory cranes mounted on a common track. The cranes must complete a sequence of tasks at locations along the track without crossing paths, while adhering as closely as possible to a factory production schedule. The algorithm creates a decision tree of possible states of the crane… (More)
What can MDDs do for combinatorial optimization? • Compact representation of all solutions to a problem • Limit on size gives approximation • Control strength of approximation by size limit MDDs for integer optimization • MDD relaxations provide upper bounds • MDD restrictions provide lower bounds • New branch‐and‐bound scheme MDDs for constraint‐based… (More)