William J. Cook

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We propose new methodologies in robust optimization that promise greater tractability, both theoretically and practically than the classical robust framework. We cover a broad range of mathematical optimization problems, including linear optimization (LP), quadratic constrained quadratic optimization (QCQP), general conic optimization including second order(More)
Chvfital introduced the idea of viewing cutting planes as a system for proving that every integral solution of a given set of linear inequalities satisfies another given linear inequality. This viewpoint has proven to be very useful in many studies of combinatorial and integer programming problems. The basic ingredient in these cutting-plane proofs is that(More)
We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained Lin-Kernighan heuristic for large-scale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of these instances, solutions within 1% of the optimal value can be(More)
The first computer implementation of the Dantzig-FulkersonJohnson cutting-plane method for solving the traveling salesman problem, written by Martin, used subtour inequalities as well as cutting planes of Gomory’s type. The practice of looking for and using cuts that match prescribed templates in conjunction with Gomory cuts was continued in computer codes(More)
The crystal structure of human erythrocytic ubiquitin has been refined at 1.8 A resolution using a restrained least-squares procedure. The crystallographic R-factor for the final model is 0.176. Bond lengths and bond angles in the molecule have root-mean-square deviations from ideal values of 0.016 A and 1.5 degrees, respectively. A total of 58 water(More)
We make several observations on the implementation of Edmonds’ blossom algorithm for solving minimum-weight perfectmatching problems and we present computational results for geometric problem instances ranging in size from 1,000 nodes up to 5,000,000 nodes. A key feature in our implementation is the use of multiple search trees with an individual(More)
The crystal structure of mammalian calmodulin has been refined at 2.2 A (1 A = 0.1 nm) resolution using a restrained least-squares method. The final crystallographic R-factor, based on 6685 reflections in the range 2.2 A less than or equal to d less than or equal to 5.0 A with intensities exceeding 2.5 sigma, is 0.175. Bond lengths and bond angles in the(More)