On the Application of the SCD Semismooth Newton Method to Variational Inequalities of the Second Kind

The paper starts with a description of SCD (subspace containing derivative) mappings and the SCD Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one obtains an implementable algorithm which exhi...

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Vydáno v:Set-valued and variational analysis Ročník 30; číslo 4; s. 1453 - 1484
Hlavní autoři: Gfrerer, Helmut, Outrata, Jiří V., Valdman, Jan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Dordrecht Springer Netherlands 01.12.2022
Springer Nature B.V
Témata:
Algorithms
Analysis
Convergence
Equilibrium methods
Inclusions
Inequalities
Mathematics
Mathematics and Statistics
Newton methods
Optimization
Semismoothness
Global convergence
65K15
Generalized equation
90C33
Superlinear convergence
65K10
Newton method
Coderivatives
ISSN:1877-0533, 1877-0541
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Shrnutí:The paper starts with a description of SCD (subspace containing derivative) mappings and the SCD Newton method for the solution of general inclusions. This method is then applied to a class of variational inequalities of the second kind. As a result, one obtains an implementable algorithm which exhibits locally superlinear convergence. Thereafter we suggest several globally convergent hybrid algorithms in which one combines the SCD Newton method with selected splitting algorithms for the solution of monotone variational inequalities. Finally, we demonstrate the efficiency of one of these methods via a Cournot-Nash equilibrium, modeled as a variational inequality of the second kind, where one admits really large numbers of players (firms) and produced commodities.
Bibliografie:ObjectType-Article-1
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ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-022-00651-2