Search results for "BDIFF"

showing 3 items of 13 documents

Convergence rate of a relaxed inertial proximal algorithm for convex minimization

2018

International audience; In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim to solve monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for values which have similarities with the results based on the Nesterov accelerated gradient method. The joint adjustment of inertia, relaxation and proximal terms plays a central role. In doing so, we highlight inertial proximal algorithms that converge for general monotone inclusions, and which, in the case of convex minimization, give fast convergence rates of values in the worst case.

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]Class (set theory)Control and OptimizationInertial frame of referenceLyapunov analysis0211 other engineering and technologies02 engineering and technologyManagement Science and Operations Research01 natural sciencessymbols.namesakenonsmooth convex minimizationrelaxationweak-convergence0101 mathematics[MATH]Mathematics [math]point algorithmMathematics021103 operations researchWeak convergence[QFIN]Quantitative Finance [q-fin]Applied MathematicsHilbert space[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]dynamicsmaximally monotone operatorsInertial proximal method010101 applied mathematicsMonotone polygonRate of convergenceConvex optimizationmaximal monotone-operatorssymbolsRelaxation (approximation)[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]subdifferential of convex functionsAlgorithm
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Differential inclusions involving normal cones of nonregular sets in Hilbert spaces

2017

This thesis is dedicated to the study of differential inclusions involving normal cones of nonregular sets in Hilbert spaces. In particular, we are interested in the sweeping process and its variants. The sweeping process is a constrained differential inclusion involving normal cones which appears naturally in several applications such as elastoplasticity, electrical circuits, hysteresis, crowd motion, etc.This work is divided conceptually in three parts: Study of positively alpha-far sets, existence results for differential inclusions involving normal cones and characterizations of Lyapunov pairs for the sweeping process. In the first part (Chapter 2), we investigate the class of positivel…

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]cône normalMoreau-Yosida regularizationcono normalmétodo de tipo Galerkinfonction distanceGalerkin-like methodMSC: 34A60 49J52 34G25 49J53 34B10 93D30subdiferencial de Clarkeprocessus de rafleInclusión diferencialensembles positivement alpha-far'sweeping processfonctions de Lyapunovsous-différentiel de Clarkeprocesos de arrastrefunción distanciaLyapunov functionsconjuntos positivamente alpha-farFunciones de Lyapunovméthode de type Galerkinrégularisation de Moreau-YosidaDifferential inclusions[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Clarke subdifferentialregularización de Moreau-YosidaDistance functionInclusion différentielle[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]Normal conepositively alpha-far sets
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Decay estimates for time-fractional and other non-local in time subdiffusion equations in R^d

2016

We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in R d . An important special case is the timefractional diffusion equation, which has seen much interest during the last years, mostly due to its applications in the modeling of anomalous diffusion processes. We follow three different approaches and techniques to study this particular case: (A) estimates based on the fundamental solution and Young’s inequality, (B) Fourier multiplier methods, and (C) the energy method. It turns out that the decay behaviour is markedly different from the heat equation case, in particular there occurs a critical dimension phenom…

fundamental solutionFourier multipliersubdiffusionenergy estimatestime-fractional diffusionultraslow diffusionsubordinationtemporal decay estimates
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