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

We all want to maximize our gains and minimize our losses, but decisions have uncertain outcomes. What if you could choose between an expected return of $1000 with no chance of losing any amount, or an expected return of $5000 with a chance of losing $50,000. Which would you choose? The answer depends upon how risk-averse you are. Many would happily take… (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)

- 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)

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)

- 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, André Rohe
- INFORMS Journal on Computing
- 1999

A perfect matching in a graph G is a subset of edges such that each node in G is met by exactly one edge in the subset. Given a real weight c e for each edge e of G, the minimum-weight perfect-matching problem is to find a perfect matching M of minimum weight ͚(c e Ϻe ʦ M). One of the fundamental results in combinatorial optimization is the polynomial-time… (More)

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