Abstract
The auxiliary problem principle introduced by Cohen is extended to a general equilibrium problem. In particular, applications to variational inequalities and to convex optimization problems are analysed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Blum and W. Oettli, From Optimization and Variational Inequalities to Equilibrium Problems, The Mathematics Student, Vol. 63, 1–23, 1993;
G. Chen and R.T. Rockafellar, Convergence Rates in Forward-Backward Splitting, SIAM Journal of Optimization, Vol. 7, 421–444, 1997;
G. Cohen, Auxiliary Problem Principle and Decomposition of Optimization Problems, Journal of Optimization Theory and Applications, Vol. 32, 277–305, 1980;
G. Cohen, Auxiliary Problem Principle Extended to Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 59, 325–333, 1988;
I. Ekeland and R. Temam, Convex Analysis and Variational Problems, North-Holland, Amsterdam, 1977;
E.N. Farouq and G. Cohen, Progressive Regularization of Variational Inequalities and Decomposition Algorithms, Journal of Optimization Theory and Applications, Vol. 97, 407–433, 1998;
F. Giannessi, Separation of sets and Gap Functions for Quasi-Variational Inequalities, in “Variational Inequalities and Network Equilibrium Problems”, F. Giannessi and A. Maugeri (eds), Plenum Publishing Co, 101–121, 1995;
F. Giannessi, Vector Variational Inequalities and Vector Equilibria, Kluwer Acad. Publ., Dordrecht, Boston, London, 2000;
P.T. Harker, J.S. Pang, Finite—Dimensional Variational Inequalities and Nonlinear Complementarity Problem: a Survey of Theory, Algorithms and Applications, Mathematical Programming, Vol. 48, 161–220, 1990;
S. Karamardian, An Existence Theorem for the Complementary Problem, Journal of Optimization Theory and Applications,Vol. 18, 445–454, 1976;
G. Mastroeni, Minimax and extremum problems associated to a Variational Inequality, Supplemento ai Rendiconti del Circolo Matematico di Palermo, Suppl. 58, 185–196, 1999;
A. Moudafi, Proximal Point Algorithm Extended to Equilibrium Problems, Journal of Natural Geometry,Vol. 15, 91–100, 1999;
R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, 1970.
G. Salmon, V.H. Nguyen and J.J. Strodiot, Coupling the Auxiliary Problem Principle and Epiconvergence Theory to Solve General Variational Inequalities, Journal of Optimization Theory and Applications, Vol. 104, 629–657, 2000.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Kluwer Academic Publishers
About this chapter
Cite this chapter
Mastroeni, G. (2003). On Auxiliary Principle for Equilibrium Problems. In: Daniele, P., Giannessi, F., Maugeri, A. (eds) Equilibrium Problems and Variational Models. Nonconvex Optimization and Its Applications, vol 68. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0239-1_15
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0239-1_15
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7955-3
Online ISBN: 978-1-4613-0239-1
eBook Packages: Springer Book Archive