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MIERCURI, 07.04.2021, la ora 13.30, la Facultatea de Matematic\u0103 \u0219i Informatic\u0103\u00a0a avut loc SEMINARUL ONLINE<\/strong><\/p>\n cu invitatul special\u00a0Pierre-Antoine Absil,<\/strong><\/h2>\n Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM<\/a>),\u00a0<\/strong><\/p>\n Louvain School of Engineering<\/a>\u00a0University of Louvain<\/a>, Belgium.\u00a0https:\/\/sites.uclouvain.be\/absil\/<\/a><\/strong><\/p>\n <\/p>\n ABSTRACT:<\/p>\n This talk concerns applications of differential geometry in numerical In the recent years, the practical importance of optimization problems MIERCURI, 07.04.2021, la ora 13.30, la Facultatea de Matematic\u0103 \u0219i Informatic\u0103\u00a0a avut loc SEMINARUL ONLINE Introduction to optimization on manifolds cu invitatul special\u00a0Pierre-Antoine Absil, Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM),\u00a0 Louvain School of Engineering\u00a0University of Louvain, Belgium.\u00a0https:\/\/sites.uclouvain.be\/absil\/ ABSTRACT: This talk concerns applications of differential geometry in numerical optimization. They… Introduction to optimization on manifolds<\/p>\n
\noptimization. They arise when the optimization problem can be formulated
\nas finding an optimum of a real-valued cost function defined on a smooth
\nnonlinear search space. Oftentimes, the search space is a “matrix
\nmanifold”, in the sense that its points admit natural representations in
\nthe form of matrices. In most cases, the matrix manifold structure is
\ndue either to the presence of certain nonlinear constraints (such as
\northogonality or rank constraints), or to invariance properties in the
\ncost function that need to be factored out in order to obtain a
\nnondegenerate optimization problem. Manifolds that come up in practical
\napplications include the rotation group SO(3) (generation of rigid body
\nmotions from sample points), the set of fixed-rank matrices (low-rank
\nmodels, e.g., in collaborative filtering), the set of 3×3 symmetric
\npositive-definite matrices (interpolation of diffusion tensors), and the
\nshape manifold (morphing).<\/p>\n
\non manifolds has stimulated the development of geometric optimization
\nalgorithms that exploit the differential structure of the manifold
\nsearch space. In this talk, we give an overview of geometric
\noptimization algorithms and their applications, with an emphasis on the
\nunderlying geometric concepts and on the numerical efficiency of the
\nalgorithm implementations.<\/p>\n","protected":false},"excerpt":{"rendered":"
Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_theme","meta":{"_seopress_robots_primary_cat":"","_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","footnotes":""},"class_list":["post-1068","page","type-page","status-publish","hentry"],"rttpg_featured_image_url":null,"rttpg_author":{"display_name":"","author_link":"https:\/\/fmi.usm.md\/en\/author\/"},"rttpg_comment":0,"rttpg_category":null,"rttpg_excerpt":"MIERCURI, 07.04.2021, la ora 13.30, la Facultatea de Matematic\u0103 \u0219i Informatic\u0103\u00a0a avut loc SEMINARUL ONLINE Introduction to optimization on manifolds cu invitatul special\u00a0Pierre-Antoine Absil, Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM),\u00a0 Louvain School of Engineering\u00a0University of Louvain, Belgium.\u00a0https:\/\/sites.uclouvain.be\/absil\/ ABSTRACT: This talk concerns applications of differential geometry in numerical optimization. They……","_links":{"self":[{"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/pages\/1068","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/comments?post=1068"}],"version-history":[{"count":1,"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/pages\/1068\/revisions"}],"predecessor-version":[{"id":1070,"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/pages\/1068\/revisions\/1070"}],"wp:attachment":[{"href":"https:\/\/fmi.usm.md\/en\/wp-json\/wp\/v2\/media?parent=1068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}