AbstractWe provide two certificates of convexity for arbitrary basic closed semi-algebraic sets of Rn. The first one is based on a necessary and sufficient condition whereas the second one is based on a sufficient (but simpler) condition only. Both certificates are obtained from any feasible solution of a related semidefinite program and so, in principle, can be obtained numerically (however, up to machine precision)
The first part of this thesis deals with infeasibility in semidefinite programs (SDPs). In SDP, unli...
For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding ...
Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geo...
AbstractWe provide two certificates of convexity for arbitrary basic closed semi-algebraic sets of R...
International audienceWe provide two certificates of convexity for arbitrary basic semi-algebraic se...
Abstract. A set S ⊆ Rn is called to be semidefinite programming (SDP) representable if S equals the ...
The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization ...
AbstractGiven a polynomial x∈Rn↦p(x) in n=2 variables, a symbolic-numerical algorithm is first descr...
Mathematical Programming, Series A. Published electronically on May 7th 2008International audienceWe...
A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible ...
Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof comple...
33 pages, 2 figures, 5 tablesInternational audienceIn a first contribution, we revisit two certifica...
International audienceLet \Gamma be a structure with a finite relational signature and a first-order...
The goal of the current paper is to introduce the notion of certificates which verify the accuracy o...
We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinit...
The first part of this thesis deals with infeasibility in semidefinite programs (SDPs). In SDP, unli...
For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding ...
Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geo...
AbstractWe provide two certificates of convexity for arbitrary basic closed semi-algebraic sets of R...
International audienceWe provide two certificates of convexity for arbitrary basic semi-algebraic se...
Abstract. A set S ⊆ Rn is called to be semidefinite programming (SDP) representable if S equals the ...
The Lasserre hierarchy of semidefinite programming approximations to convex polynomial optimization ...
AbstractGiven a polynomial x∈Rn↦p(x) in n=2 variables, a symbolic-numerical algorithm is first descr...
Mathematical Programming, Series A. Published electronically on May 7th 2008International audienceWe...
A hierarchy of convex relaxations for semialgebraic problems is introduced. For questions reducible ...
Inspired by branch-and-bound and cutting plane proofs in mixed-integer optimization and proof comple...
33 pages, 2 figures, 5 tablesInternational audienceIn a first contribution, we revisit two certifica...
International audienceLet \Gamma be a structure with a finite relational signature and a first-order...
The goal of the current paper is to introduce the notion of certificates which verify the accuracy o...
We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinit...
The first part of this thesis deals with infeasibility in semidefinite programs (SDPs). In SDP, unli...
For an arbitrary finite family of semi-algebraic/definable functions, we consider the corresponding ...
Convex algebraic geometry concerns the interplay between optimization theory and real algebraic geo...
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