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- Aharon Ben-Tal, Laurent El Ghaoui, +14 authors ROBook May
- 2004

We propose new methodologies in robust optimization that promise greater tractabil-ity, 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… (More)

- David Applegate, William J. Cook
- INFORMS Journal on Computing
- 1991

- William J. Cook, Ravi Kannan, Alexander Schrijver
- Math. Program.
- 1990

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)

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)

- S Vijay-Kumar, C E Bugg, W J Cook
- Journal of molecular biology
- 1987

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)

Following the theoretical studies of J.B. Robinson and H.W. Kuhn in the late 1940s and the early 1950s, G.B. Dantzig, R. Fulk-erson, and S.M. Johnson demonstrated in 1954 that large instances of the TSP could be solved by linear programming. Their approach remains the only known tool for solving TSP instances with more than several hundred cities; over the… (More)

- David Applegate, Robert E. Bixby, Vasek Chvátal, William J. Cook
- Computational Combinatorial Optimization
- 2001

The rst computer implementation of the Dantzig-Fulkerson-Johnson 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)

- William J. Cook, Sanjeeb Dash
- Math. Oper. Res.
- 2001

Lovász and Schrijver (1991) described a semi-definite operator for generating strong valid inequalities for the 0-1 vectors in a prescribed polyhedron. Among their results, they showed that n iterations of the operator are sufficient to generate the convex hull of 0-1 vectors contained in a polyhedron in n-space. We give a simple example, having Chvátal… (More)

- Stephan Held, William J. Cook, Edward C. Sewell
- Math. Program. Comput.
- 2012

The best method known for determining lower bounds on the ver-tex coloring number of a graph is the linear-programming column-generation technique, where variables correspond to stable sets, first employed by Mehro-tra and Trick in 1996. We present an implementation of the method that provides numerically-safe results, independent of the floating-point… (More)

- William J. Cook, Paul D. Seymour
- INFORMS Journal on Computing
- 2003