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.
http://hdl.handle.net/2158/1101549
Titolo: | A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties |
Autori di Ateneo: | |
Autori: | GALLI, LEONARDO; Kanzow, Christian; SCIANDRONE, MARCO |
Anno di registrazione: | 2018 |
Rivista: | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS |
Volume: | 69 |
Pagina iniziale: | 629 |
Pagina finale: | 652 |
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. |
Handle: | http://hdl.handle.net/2158/1101549 |
Appare nelle tipologie: | 1a - Articolo su rivista |
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