Asymptotic for the perturbed heavy ball system with vanishing damping\n term

2016/09/01 by Mounir Balti, Balti, Mounir, Ramzi May +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1609.00135

openalex publication_date 2016/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the long time behavior of solutions to the differential\nequation \x(t)+ fracc\( t+1\) ^\α\x(t)+\∇\n\Φ\( x(t)\) =g(t),~t\≥0, where c is nonnegative constant,\n\α\∈ lbrack0,1[, \Φ is a C¹ convex function on a Hilbert space\n\H and g\∈ L¹ (0,+\∞;\H). We obtain sufficient\nconditions on the source term g(t) ensuring the weak or the strong\nconvergence of any trajectory x(t) as t\→+\∞ to a minimizer of\nthe function \Φ if one exists.\n

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