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DTSTART;TZID=Europe/Berlin:20170515T160000
DTEND;TZID=Europe/Berlin:20170515T180000
DTSTAMP:20170427T082452Z
CREATED:20170403T131431Z
LAST-MODIFIED:20170427T082452Z
UID:1158-1494864000-1494871200@alop.uni-trier.de
SUMMARY:ALOP Colloquium with Prof. Andreas Frommer
DESCRIPTION:On Monday\, May 15 2017\,   Prof. Andreas Frommer of Bergische Universität Wuppertal will join the ALOP-Colloquium and present his recent work entitled \n  \nMatrix functions – computation and convergence for Krylov subspace based methods  \nAbstract: f(A)b\, the action of the function f of a matrix A on a vector b\, is required in many applications\, for example in exponential integrators\, where f = exp or in lattice QCD where f(z) = z-α; α ϵ (0\, 1). Typically\, A is large and sparse\, so computing f(A) directly is not possible\, but subspace techniques allow to approximate f(A)b. In this talk will address issues related to the computation and to theconvergence analysis for Krylov subspace based methods. The outstanding problem in computation is how to obtain a stable restart procedure\, and we show how this can be achieved when f can be adequately represented by a contour integral. On the analytical side\, we present convergence results when f is a Stieltjes function and A is symmetric and positive denite and\, with appropriate modications\, when A is just positive denite but not necessarily symmetric. Finally\, we will address generalizations to the block case\, i.e. when several vectors b are to be treated simultaneously. \nThe presentation will take place in HS 9 \nWe will meet over coffee in E10 at 15:45
URL:https://alop.uni-trier.de/event/alop-colloquium-with-prof-frommer/
LOCATION:Trier University E Building\, Universitätsring 15\, Trier\, 54296\, Germany
CATEGORIES:Colloquium
ORGANIZER;CN="Research Training Group ALOP at Trier University":MAILTO:OptimizationDays@uni-trier.de
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DTSTART;TZID=Europe/Berlin:20170529T160000
DTEND;TZID=Europe/Berlin:20170529T180000
DTSTAMP:20170518T142057Z
CREATED:20170206T104751Z
LAST-MODIFIED:20170518T142057Z
UID:1029-1496073600-1496080800@alop.uni-trier.de
SUMMARY:ALOP Colloquium with Prof. François Glineur
DESCRIPTION:On Monday\, May 29\, 2017\,  Prof. François Glineur from the Université catholique de Louvain will join the ALOP-Colloquium and present his recent work entitled \nPerformance estimation of first-order methods for composite convex optimization \nComposite convex optimization consists in the minimization of a convex objective function equal to the sum of several convex functions with different properties\, for example a smooth term and a nonsmooth term. We consider a large class of first-order methods designed to solve such composite problems\, which rely on specific oracles for each term. We show that the worst-case performance of each of those methods can be computed exactly by solving a semidefinite optimization problem\, which also produces an explicit problem instance for which this worst-case is attained. \nThe performance estimation methodology was born in the original work of Drori and Teboulle in 2014\, which introduced a semidefinite relaxation to study the behaviour of first-order optimization algorithms for smooth unconstrained convex optimization. In this talk\, we present a framework that produces exact convergence bounds for fixed-step linear first-order methods applied to general composite convex optimization. These methods include classical and accelerated gradient methods (including constrained and proximal variants)\, conditional gradient and subgradient methods\, and also allow inexact gradient computations. \nIn particular\, our approach allows us to derive exact convergence rates for the proximal gradient method in function value\, gradient residual norm and distance to the solution\, backed by independently-checkable analytical proofs. We also use numerical computations to obtain worst-case rates for several well-known methods including accelerated gradient and the conditional gradient method\, improving on the best published rates. We conclude with a quick overview of a MATLAB toolbox implementing our framework\, called PESTO (Performance Estimation Toolbox)\, available from https://github.com/AdrienTaylor/Performance-Estimation-Toolbox \nThis is a joint work with Adrien B. Taylor and Julien M. Hendrickx\, Université catholique de Louvain\, Belgium \n  \nThe presentation will take place in HS 9.
URL:https://alop.uni-trier.de/event/alop-colloquium-with-prof-francois-glineur/
LOCATION:Trier University\, E Building\, Universitätsring 15\, Trier\, Germany
CATEGORIES:Colloquium
ORGANIZER;CN="Research Training Group ALOP at Trier University":MAILTO:OptimizationDays@uni-trier.de
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