On the Use of Elliptic Regularity Theory for the Numerical Solution of Variational Problems

Axel Dreves (), Joachim Gwinner () and Nina Ovcharova ()
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Axel Dreves: Universität der Bundeswehr München
Joachim Gwinner: Universität der Bundeswehr München
Nina Ovcharova: Universität der Bundeswehr München

A chapter in Operations Research, Engineering, and Cyber Security, 2017, pp 231-257 from Springer

Abstract: Abstract In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus on a class of elliptic multiobjective optimal control problems that can be formulated as jointly convex generalized Nash equilibrium problems (GNEPs) and on nonsmooth boundary value problems that stem from contact mechanics leading to elliptic variational inequalities (VIs).

Keywords: Complementarity problem; Dual mixed formulation; Elliptic boundary value problem; Jointly convex generalized Nash equilibrium problem; Lagrange multiplier; Multiobjective optimal control; Normalized Nash equilibrium; Obstacle problem; Saddle point formulation; Signorini problem; Smooth domain; Unilateral contact; Variational inequality; 90C29; 90C33; 49J21; 49N60 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-51500-7_11

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DOI: 10.1007/978-3-319-51500-7_11

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