$D$-gap functions and descent methods for a~class of monotone equilibrium problems
Lobachevskii journal of mathematics, Tome 13 (2003), pp. 57-65.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a general class of monotone equilibrium problems, which involve nonsmooth convex functions, in a real Banach space. We combine the $D$-gap function approach and regularization techniques and suggest a descent type algorithm to find solutions to the initial problem.
@article{LJM_2003_13_a6,
     author = {I. V. Konnov and O. V. Pinyagina},
     title = {$D$-gap functions and descent methods for a~class of monotone equilibrium problems},
     journal = {Lobachevskii journal of mathematics},
     pages = {57--65},
     publisher = {mathdoc},
     volume = {13},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2003_13_a6/}
}
TY  - JOUR
AU  - I. V. Konnov
AU  - O. V. Pinyagina
TI  - $D$-gap functions and descent methods for a~class of monotone equilibrium problems
JO  - Lobachevskii journal of mathematics
PY  - 2003
SP  - 57
EP  - 65
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2003_13_a6/
LA  - en
ID  - LJM_2003_13_a6
ER  - 
%0 Journal Article
%A I. V. Konnov
%A O. V. Pinyagina
%T $D$-gap functions and descent methods for a~class of monotone equilibrium problems
%J Lobachevskii journal of mathematics
%D 2003
%P 57-65
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2003_13_a6/
%G en
%F LJM_2003_13_a6
I. V. Konnov; O. V. Pinyagina. $D$-gap functions and descent methods for a~class of monotone equilibrium problems. Lobachevskii journal of mathematics, Tome 13 (2003), pp. 57-65. http://geodesic.mathdoc.fr/item/LJM_2003_13_a6/

[1] C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities: Applications to Free Boundary Problems, John Wiley and Sons, New York, 1984 | MR | Zbl

[2] M. Bianchi and S. Schaible, “Generalized monotone bifunctions and equilibrium problems”, J. Optim. Theory Appl., 90 (1996), 31–43 | DOI | MR | Zbl

[3] E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems”, The Mathem. Student, 63 (1994), 123–145 | MR | Zbl

[4] I. V. Konnov and S. Schaible, “Duality for equilibrium problems under generalized monotonicity”, J. Optim. Theory Appl., 104 (2000), 395–408 | DOI | MR | Zbl

[5] O. Chadli, I. V. Konnov, and J. C. Yao, “Descent method for equilibrium problems in a Banach space”, Comput. Math. Appl., 48:3–4 (2004), 609–616 | DOI | MR | Zbl

[6] I. V. Konnov and O. V. Pinyagina, “$D$-gap functions for a class of equilibrium problems in Banach spaces”, Computational Methods in Applied Mathematics, 3:2 (2003), 274–286 | MR | Zbl

[7] I. V. Konnov and O. V. Pinyagina, “The method of descent over an interval function for nonsmooth equilibrium problems”, Russ. Math. (Iz. VUZ), 47:12 (2003), 67–73 | MR | Zbl

[8] I. V. Konnov and S. Kum, “Descent methods for mixed variational inequalities in a Hilbert space”, Nonlinear Analysis: Theory, Methods and Applications, 47 (2001), 561–572 | DOI | MR | Zbl

[9] A. B. Bakushinskii and A. V. Goncharskii, Iterative Solution Methods for Ill-Posed Problems, Nauka, Moscow, 1989 (in Russian) | MR

[10] I. V. Konnov, “On a class of $D$-gap functions for mixed variational inequalities”, Russ. Math. (Iz. VUZ), 43:12 (1999), 60–64 | MR | Zbl

[11] I. V. Konnov, Combined Relaxation Methods for Variational Inequalities, Springer-Verlag, Berlin, 2001 | MR

[12] T. Parthasarathy and T. E. S. Raghavan, Some Topics in Two-person Games, Elsevier, New York, 1977

[13] B. T. Polyak, Introduction to Optimization, Optimization Software, New York, 1987 | MR