245documents trouvés
A "joint+marginal" approach to parametric optimization
J.B.LASSERRE
MAC
Conférence invitée : Advanced Methods and Perspectives in Optimization and Control (RTRA STAE), Toulouse (France), 3-5 Février 2010 , N° 10922
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124340Optimisation globale polynomiale appliquée à la rectification projective d'images non calibrées
F.BUGARIN, D.HENRION, T.SENTENAC, J.B.LASSERRE, J.J.ORTEU
CROMeP , MAC, RAP
Manifestation avec acte : French Conference on Pattern Recognition and Artificial Intelligence (RFIA 2010), Caen (France), 19-22 Janvier 2010, 8p. , N° 09774
Lien : http://hal.archives-ouvertes.fr/hal-00420081/fr/
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122022Moments, Positive Polynomials and their Applications
J.B.LASSERRE
MAC
Ouvrage (auteur) : Imperial College Press. Optimization Series Vol 1, N°ISBN : 978-1-84816-445-1, Octobre 2009, pp.1-384 , N° 09814
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120163Moments and sums of squares for polynomial optimization and related problems
J.B.LASSERRE
MAC
Revue Scientifique : Journal of Global Optimization, Vol.45, N°1, pp.39-61, Septembre 2009 , N° 09526
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Abstract
We briefly review the duality between moment problems and sums of squares (s.o.s.) representations of positive polynomials, and compare s.o.s. versus nonnegative polynomials. We then describe how to use such results to define convergent semidefinite programming relaxations in polynomial optimization as well as for the two related problems of computing the convex envelope of a rational function and finding all zeros of a system of polynomial equations.
Mots-Clés / Keywords
measures; Moments;
Approximate volume and integration for basic semi-algebraic sets
D.HENRION, J.B.LASSERRE, C.SAVORGNAN
MAC
Revue Scientifique : SIAM Review, Vol.51, N°4, pp.722-743, Septembre 2009 , N° 08391
Lien : http://hal.archives-ouvertes.fr/hal-00297384/fr/
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Abstract
Given a basic compact semi-algebraic set $K$ in $R^n$ we introduce a methodology that provides a sequence converging to the volume of $K$. This sequence is obtained from optimal values of a hierarchy of either semidefinite or linear programs. Not only the volume but also every finite vector of moments of the probability measure uniformly distributed on $K$ can be approximated as closely as desired, and so permits to approximate the integral on $K$ of any given polynomial; extension to integration against some weight functions is also provided. Finally, some numerical aspects are discussed.
Mots-Clés / Keywords
Computational geometry; Volume; Integration; K-moment problem; Semidefinite programming;
Convex sets with semidefinite représentation
J.B.LASSERRE
MAC
Revue Scientifique : Mathematical Programming, Vol.120, N°2, pp.457-477, Septembre 2009 , N° 07034
Lien : http://hal.archives-ouvertes.fr/hal-00331665/fr/
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Abstract
We provide a sufficient condition on a class of compact basic semialgebraic sets K for their convex hull co(K) to have a semidefinite representation (SDr). This SDr is explicitly expressed in terms of the polynomials (g_j) that define K. Examples are provided. We also provide an approximate SDr; that is, for every fixed epsilon>0 there is a convex set K_epsilon in sandwich between co(K) and co(K)+epsilon B (where B is the unit ball of R_n) and K_epsilon has an explicit SDr in terms of the g_j's. For convex and compact basic semi-algebraic sets K defined by concave polynomials, we provide a simpler explicit SDr when the nonnegative Lagrangian L_f associated with K and any linear polynomial f, is a sum of squares. We also provide an approximate SDr specific to the convex case.
Mots-Clés / Keywords
Lifted semidefinite representation; Semi-algbraic set;
GloptiPoly 3: moments, optimization and semidefinite programming
D.HENRION, J.B.LASSERRE, J.LOFBERG
MAC, ETH-ETL
Revue Scientifique : Optimization Methods and Software, Vol.24, N°4-5, pp.761-779, Août 2009 , N° 07536
Lien : http://hal.archives-ouvertes.fr/hal-00172442/fr/
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Abstract
We describe a major update of our Matlab freeware GloptiPoly for parsing generalized problems of moments and solving them numerically with semidefinite programming.
POCP: a package for polynomial optimal control problems
D.HENRION, J.B.LASSERRE, C.SAVORGNAN
KUL, MAC
Manifestation avec acte : European Control Conference (ECC09), Budapest (Hongrie), 23-27 Août 2009, 17p. , N° 08647
Lien : http://hal.archives-ouvertes.fr/hal-00325180/fr/
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Abstract
POCP is a new Matlab package running jointly with GloptiPoly 3 and, optionally, YALMIP. It is aimed at nonlinear optimal control problems for which all the problem data are polynomial, and provides an approximation of the optimal value as well as some control policy. Thanks to a user-friendly interface, POCP reformulates such control problems as generalized problems of moments, in turn converted by GloptiPoly 3 into a hierarchy of semidefinite programming problems whose associated sequence of optimal values converges to the optimal value of the polynomial optimal control problem. In this paper we describe the basic features of POCP and illustrate them with some numerical examples.
Mots-Clés / Keywords
Optimal control; Polynomial; Software package; Computer-aided control system design;
A prolongation-projection algorithm for computing the finite real variety of an ideal
J.B.LASSERRE, M.LAURENT, P.ROSTALSKI
MAC, ACL Zurich, CWI, Amsterdam
Revue Scientifique : Theoretical Computer Science, Vol.410, N°27-29, pp.2685-2700, Juin 2009 , N° 09324
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117948A unified methodology for real and complex zeros of zero-dimensional ideals
J.B.LASSERRE, M.LAURENT, P.ROSTALSKI
MAC, Kruislaan, ACL Zurich
Ouvrage (contribution) : Emerging Applications of Algebraic Geometry, Springer, 380p., N°ISBN: 978-0-387-09685-8, 2009, pp.125-156 , N° 07647
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Mots-Clés / Keywords
Polynomial ideal; Zero-dimensional ideal; Complex roots; Real roots; Numerical linear algebra;