We consider equilibrium problems with differentiable bifunctions. We adopt the well-known approach based on the reformulation of the equilibrium problem as a global optimization problem through an appropriate gap function. We propose a solution method based on the inexact (and hence, less expensive) evaluation of the gap function and on the employment of a nonmonotone line search. We prove global convergence properties of the proposed inexact method under standard assumptions. Some preliminary numerical results show the potential computational advantages of the inexact method compared with a standard exact descent method. © 2013 Taylor and Francis.

A convergent inexact solution method for equilibrium problems / Di Lorenzo, D.; Passacantando, M.; Sciandrone, M.. - In: OPTIMIZATION METHODS & SOFTWARE. - ISSN 1055-6788. - 29:5(2014), pp. 979-991. [10.1080/10556788.2013.796376]

A convergent inexact solution method for equilibrium problems

Passacantando M.;Sciandrone M.
2014

Abstract

We consider equilibrium problems with differentiable bifunctions. We adopt the well-known approach based on the reformulation of the equilibrium problem as a global optimization problem through an appropriate gap function. We propose a solution method based on the inexact (and hence, less expensive) evaluation of the gap function and on the employment of a nonmonotone line search. We prove global convergence properties of the proposed inexact method under standard assumptions. Some preliminary numerical results show the potential computational advantages of the inexact method compared with a standard exact descent method. © 2013 Taylor and Francis.
2014
equilibrium problem; gap function; inexact method; nonmonotone line search
01 Pubblicazione su rivista::01a Articolo in rivista
A convergent inexact solution method for equilibrium problems / Di Lorenzo, D.; Passacantando, M.; Sciandrone, M.. - In: OPTIMIZATION METHODS & SOFTWARE. - ISSN 1055-6788. - 29:5(2014), pp. 979-991. [10.1080/10556788.2013.796376]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1625739
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