Van, N. T. T., Strodiot, J. J., Nguyen, V. H., & Phan, V. (2018). An extragradient-type method for solving nonmonotone quasi-equilibrium problems. Optimization, 67(5), 651–664. https://doi.org/10.1080/02331934.2017.1416610
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Journal:
Optimization
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ISSN:
0233-1934
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Date (published):
2018
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Number of Pages:
14
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Publisher:
TAYLOR & FRANCIS LTD
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Peer reviewed:
Yes
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Keywords:
Applied Mathematics; convergence; Control and Optimization; Management Science and Operations Research; Extragradient-type method; quasi-equilibrium problem; nonmonotone operator
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Abstract:
In this paper, a quasi-equilibrium problem with a nonmonotone bifunction is considered in a finite-dimensional space. The primary difficulty with this problem is related to the fact that one must simultaneously solve a nonmonotone equilibrium problem and calculate a fixed point of a multivalued mapping. An extragradient-type method is presented and analysed for its solution. The convergence of the method is proved under the assumption that the solution set of an associated dual equilibrium problem is nonempty. Finally, some numerical experiments are reported.
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Research Areas:
Fundamental Mathematics Research: 30% Mathematical and Algorithmic Foundations: 70%