Variational discretization and semi-smooth Newton methods; implementation, convergence and globalization in pde constrained optimization with control constraints

2009/12/02 by Michael Hinze, Hinze, Michael, Morten Vierling +1 · 3 citations
Computer Science · Mathematics · #49J20 #49K20 #49M15 #Advanced Optimization Algorithms Research #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC #msc:49J20 #msc:49K20 #msc:49M15

paper · pdf · doi:10.48550/arxiv.0912.0488

arxiv created 2009/12/02 · openalex publication_date 2009/12/02 · arxiv updated 2009/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

When combining the numerical concept of variational discretization and semi-smooth Newton methods for the numerical solution of pde constrained optimization with control constraints, special emphasis has to be taken on the implementation, convergence and globalization of the numerical algorithm. In the present work we address all these issues. In particular we prove fast local convergence of the algorithm and propose two different globalization strategies which are applicable in many practically relevant mathematical settings. We illustrate our analytical and algorithmical findings by numerical experiments.

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