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- Etienne de Klerk, Dmitrii V. Pasechnik
- SIAM Journal on Optimization
- 2002

Lovasz and Schrijver [SIAM J. Optim., 1 (1991), pp. 166--190] showed how to formulate increasingly tight approximations of the stable set polytope of a graph by solving semidefinite programs (SDPs)… (More)

Solving Standard Quadratic Optimization Problems via Linear, Semidefinite and Copositive Programming

- Immanuel M. Bomze, Etienne de Klerk
- J. Global Optimization
- 2002

The problem of minimizing a (non-convex) quadratic function over the simplex (the standard quadratic optimization problem) has an exact convex reformulation as a copositive programming problem. In… (More)

- Etienne de Klerk
- 2002

Acknowledgments. List of notation. 1. Introduction. Part I: Theory and Algorithms. 2. Duality, Optimality, and Degeneracy. 3. The Central Path. 4. Self-Dual Embeddings. 5. The Primal Logarithmic… (More)

- Etienne de Klerk, Dmitrii V. Pasechnik, Alexander Schrijver
- Math. Program.
- 2007

AbstractWe consider semidefinite programming problems on which a permutation group is acting. We describe a general technique to reduce the size of such problems, exploiting the symmetry. The… (More)

- Etienne de Klerk
- 2002

- Etienne de Klerk, Renata Sotirov
- Math. Program.
- 2007

We consider semidefinite programming relaxations of the quadratic assignment problem, and show how to exploit group symmetry in the problem data. Thus we are able to compute the best known lower… (More)

- Etienne de Klerk, Monique Laurent, Pablo A. Parrilo
- Theor. Comput. Sci.
- 2006

We consider the problem of computing the minimum value pmin taken by a polynomial p(x) of degree d over the standard simplex Δ. This is an NP-hard problem already for degree d = 2. For any integer k… (More)

- Etienne de Klerk, Dmitrii V. Pasechnik, Renata Sotirov
- SIAM Journal on Optimization
- 2008

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP) that may be obtained via an SDP relaxation of the more general quadratic assignment… (More)

- Immanuel M. Bomze, Mirjam Dür, Etienne de Klerk, Kees Roos, Arie J. Quist, Tamás Terlaky
- J. Global Optimization
- 2000

A standard quadratic problem consists of finding global maximizers of a quadratic form over the standard simplex. In this paper, the usual semidefinite programming relaxation is strengthened by… (More)

- Etienne de Klerk, John Maharry, Dmitrii V. Pasechnik, R. Bruce Richter, Gelasio Salazar
- SIAM J. Discrete Math.
- 2006

It has been long conjectured that the crossing number $\Cr(K_{m,n})$ of the complete bipartite graph $K_{m,n}$ equals the Zarankiewicz number $Z(m,n):= \floor{\frac{m-1}{2}} \floor{\frac{m}{2}}… (More)