A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties

Leonardo Galli (), Christian Kanzow () and Marco Sciandrone ()
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Leonardo Galli: University of Florence
Christian Kanzow: University of Würzburg
Marco Sciandrone: University of Florence

Computational Optimization and Applications, 2018, vol. 69, issue 3, No 3, 629-652

Abstract: Abstract The generalized Nash equilibrium problem (GNEP) is often difficult to solve by Newton-type methods since the problem tends to have locally nonunique solutions. Here we take an existing trust-region method which is known to be locally fast convergent under a relatively mild error bound condition, and modify this method by a nonmonotone strategy in order to obtain a more reliable and efficient solver. The nonmonotone trust-region method inherits the nice local convergence properties of its monotone counterpart and is also shown to have the same global convergence properties. Numerical results indicate that the nonmonotone trust-region method is significantly better than the monotone version, and is at least competitive to an existing software applied to the same reformulation used within our trust-region framework. Additional tests on quasi-variational inequalities (QVI) are also presented to validate efficiency of the proposed extension.

Keywords: Generalized Nash equilibrium problem; Trust-region algorithm; Nonmonotone strategy; Global convergence; Local superlinear convergence; Quasi-variational inequalities (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10589-017-9960-3

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