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Authordc.contributor.authorÁlvarez Daziano, Felipe 
Authordc.contributor.authorBolte, Jérome es_CL
Authordc.contributor.authorBrahic, Olivier es_CL
Admission datedc.date.accessioned2013-07-02T20:32:27Z
Available datedc.date.available2013-07-02T20:32:27Z
Publication datedc.date.issued2004
Cita de ítemdc.identifier.citationSIAM JOURNAL ON CONTROL AND OPTIMIZATION Volume: 43 Issue: 2 Pages: 477-501 Published: 2004en_US
Identifierdc.identifier.otherDOI: 10.1137/S0363012902419977
Identifierdc.identifier.urihttps://repositorio.uchile.cl/handle/2250/125794
General notedc.descriptionArtículo de publicación ISIen_US
Abstractdc.description.abstractIn view of solving theoretically constrained minimization problems, we investigate the properties of the gradient flows with respect to Hessian Riemannian metrics induced by Legendre functions. The first result characterizes Hessian Riemannian structures on convex sets as metrics that have a specific integration property with respect to variational inequalities, giving a new motivation for the introduction of Bregman-type distances. Then, the general evolution problem is introduced, and global convergence is established under quasi-convexity conditions, with interesting refinements in the case of convex minimization. Some explicit examples of these gradient flows are discussed. Dual trajectories are identified, and sufficient conditions for dual convergence are examined for a convex program with positivity and equality constraints. Some convergence rate results are established. In the case of a linear objective function, several optimality characterizations of the orbits are given: optimal path of viscosity methods, continuous-time model of Bregman-type proximal algorithms, geodesics for some adequate metrics, and projections of. (q) over dot-trajectories of some Lagrange equations and completely integrable Hamiltonian systems.en_US
Lenguagedc.language.isoenen_US
Publisherdc.publisherSIAM PUBLICATIONSen_US
Keywordsdc.subjectgradient flowen_US
Títulodc.titleHessian Riemannian gradient flows in convex programmingen_US
Document typedc.typeArtículo de revistaen_US


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