Regularization algorithms for solving monotone Ky Fan inequalities with application to a Nash-Cournot equilibrium model. (English) Zbl 1191.90084

The authors make use of the Banach contraction mapping principle to prove the linear convergence of a regularization algorithm for strongly monotone Ky Fan inequalities that satisfy a Lipschitz-type condition introduced in [G. Mastroeni, in: Equilibrium problems and variational models, Nonconvex Optim. Appl. 68, 289–298 (2003; Zbl 1069.49009)]. Then, they apply the algorithm to strongly monotone Lipschitzian variational inequalities. As a consequence, they obtain a new linearly convergent derivative-free algorithm for strongly monotone complementarity problems. The linear convergence rate allows the algorithm to be coupled with inexact proximal point methods for solving monotone (not necessarily strongly monotone) problems satisfying the Lipschitz-type condition mentioned above. Finally, the authors propose a line-search free algorithm for the strong monotone problem which does not require the Lipschitz-type condition. Applications to a Nash-Cournot market equilibrium model are discussed in section 6 and some preliminary computational results are reported.


90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
49J53 Set-valued and variational analysis
65K15 Numerical methods for variational inequalities and related problems
90B50 Management decision making, including multiple objectives


Zbl 1069.49009
Full Text: DOI


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