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Mathematics > Optimization and Control

arXiv:1805.03009 (math)
[Submitted on 8 May 2018 (v1), last revised 8 Nov 2018 (this version, v2)]

Title:On Non-Reducible Multi-Player Control Problems and their Numerical Computation

Authors:Veronika Karl, Frank Pörner
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Abstract:In this article we consider a special class of Nash equilibrium problems that cannot be reduced to a single player control problem. Problems of this type can be solved by a semi-smooth Newton method. Applying results from the established convergence analysis we derive superlinear convergence for the associated Newton method and the equivalent active-set method. We also provide detailed finite element discretizations for both methods. Several numerical examples are presented to support the theoretical findings.
Subjects: Optimization and Control (math.OC)
MSC classes: 49M05, 49M15, 65K10, 65K15
Cite as: arXiv:1805.03009 [math.OC]
  (or arXiv:1805.03009v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1805.03009

Submission history

From: Veronika Karl [view email]
[v1] Tue, 8 May 2018 13:39:59 UTC (1,011 KB)
[v2] Thu, 8 Nov 2018 09:02:25 UTC (462 KB)
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