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- Mikhail Deza, Monique Laurent
- Algorithms and combinatorics
- 1997

Cuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of… (More)

- Monique Laurent
- 2009

We consider the problem of minimizing a polynomial over a semialgebraic set defined by polynomial equations and inequalities, which is NP-hard in general. Hierarchies of semidefinite relaxations have… (More)

We survey how semidefinite programming can be used for finding good approximative solutions to hard combinatorial optimization problems.

- Monique Laurent
- Math. Program.
- 2007

We consider the problem of minimizing a polynomial over a set defined by polynomial equations and inequalities. When the polynomial equations have a finite set of complex solutions, we can… (More)

In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of… (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)

Abstract We study the convex set L n defined by L n Z ≔ { X | X = ( x ij ) a positive semidefinite n × n matrix, x ii = 1 for all i }. We describe several geometric properties of L n . In particular,… (More)

- Monique Laurent, Antonios Varvitsiotis
- Math. Program.
- 2012

The Gram dimension $$\mathrm{gd}(G)$$ of a graph $$G$$ is the smallest integer $$k\ge 1$$ such that any partial real symmetric matrix, whose entries are specified on the diagonal and at the… (More)

- Jean B. Lasserre, Monique Laurent, Philipp Rostalski
- Foundations of Computational Mathematics
- 2006

Abstract
For an ideal I⊆ℝ[x] given by a set of generators, a new semidefinite characterization of its real radical I(Vℝ(I)) is presented, provided it is zero-dimensional (even if I is not). Moreover,… (More)

- Dorina Jibetean, Monique Laurent
- SIAM Journal on Optimization
- 2005

We consider the problem of minimizing a polynomial function on ${\mathbb R}^n$, known to be hard even for degree 4 polynomials. Therefore approximation algorithms are of interest. Lasserre [SIAM J.… (More)