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.

A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties / Galli, L.; Kanzow, C.; Sciandrone, M.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 69:3(2018), pp. 629-652. [10.1007/s10589-017-9960-3]

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

Sciandrone M.
2018

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.
2018
Generalized Nash equilibrium problem; Global convergence; Local superlinear convergence; Nonmonotone strategy; Quasi-variational inequalities; Trust-region algorithm
01 Pubblicazione su rivista::01a Articolo in rivista
A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties / Galli, L.; Kanzow, C.; Sciandrone, M.. - In: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS. - ISSN 0926-6003. - 69:3(2018), pp. 629-652. [10.1007/s10589-017-9960-3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1625473
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