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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 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 describe a specialized dynamic programming algorithm for factory crane scheduling. An innovative data structure controls the memory requirements of the state space and enables solution of problems of realistic size. The algorithm finds optimal space-time trajectories for two factory cranes or hoists that move along a single overhead track. Each crane is(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)
This thesis addresses three topics: solving the Nash Equilibrium problem for two-player zero-sum games presented in extensive form, constraint programming using multivalued decision diagrams and scheduling cranes in a factory. In the first chapter, we develop a first-order method based on a smoothing technique of Nesterov that allows us to solve problems(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)
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