Tikhonov regularization method for a system of equilibrium problems in Banach spaces

M. Bianchi and S. Schaible, “Generalized monotone bifunctions and equilibrium problems,” J. Optimiz. Theory Appl., 90, 31–43 (1996).

E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” Math. Stud., 63, 123–145 (1994).

W. Oettli, “A remark on vector-valued equilibria and generalized monotonicity,” Acta Math. Vietnam, 22, 215–221 (1997).

A. Göpfert, H. Riahi, C. Tammer, and C. Zalinescu, Variational Methods in Partially Ordered Spaces, Springer, New York (2003).

O. Chadli, S. Schaible, and J. C. Yao, “Regularized equilibrium problems with an application to noncoercive hemivariational inequalities,” J. Optimiz. Theory Appl., 121, 571–596 (2004).

P. L. Combettes and S. A. Hirstoaga, “Equilibrium programming in Hilbert spaces,” J. Nonlin. Convex Anal., 6, No. 1, 117–136 (2005).

I. V. Konnov and O. V. Pinyagina, “D-gap functions for a class of monotone equilibrium problems in Banach spaces,” Comput. Methods Appl. Math., 3, No. 2, 274–286 (2003).

A. C. Stukalov, “Regularization extragradient method for solving equilibrium programming problems in Hilbert spaces,” Zh. Vychisl. Mat. Mat. Fiz., 45, No. 9, 1538–1554 (2005).

I. V. Konnov and O. V. Pinyagina, “D-gap functions and descent methods for a class of monotone equilibrium problems,” Lobachevskii J. Math., 13, 57–65 (2003).

G. Mastroeni, “Gap functions for equilibrium problems,” J. Global Optimiz., 27, 411–426 (2003).

A. S. Antipin, “Equilibrium programming: gradient methods,” Automat. Remote Control, 58, No. 8, 1337–1347 (1997).

A. S. Antipin, “Equilibrium programming: proximal methods,” Comput. Math. Math. Phys., 37, No. 11, 1285–1296 (1997).

M. Bounkhel and B. R. Al-Senan, “An iterative method for nonconvex equilibrium problems,” J. Inequal. Pure Appl. Math., 7, Issue 2, Article 75 (2006).

O. Chadli, I. V. Konnov, and J. C. Yao, “Descent methods for equilibrium problems in Banach spaces,” Comput. Math. Appl., 48, 609–616 (2004).

I. V. Konnov, “Application of the proximal point method to nonmonotone equilibrium problems,” J. Optimiz. Theory Appl., 126, 309–322 (2005).

I. V. Konnov, S. Schaible, and J. C. Yao, “Combined relaxation method for mixed equilibrium problems,” J. Optimiz. Theory Appl., 119, 317–333 (2003).

G. Mastroeni, “On auxiliary principle for equilibrium problems,” Techn. Rep. Dep. Math. Pisa Univ., No. 3, 244–258 (2000).

A. Moudafi, “Second-order differential proximal methods for equilibrium problems,” J. Inequal. Pure Appl. Math., 4, Issue 1, Article 18 (2003).

A. Moudafi and M. Théra, “Proximal and dynamical approaches to equilibrium problems,” Lect. Notes Econ. Math. Syst., 477, 187–201 (1999).

M. A. Noor, “Auxiliary principle technique for equilibrium problems,” J. Optimiz. Theory Appl., 122, 371–386 (2004).

M. A. Noor and K. I. Noor, “On equilibrium problems,” Appl. Math. E-Notes, 4, 125–132 (2004).

N. Buong, “Regularization for unconstrained vector optimization of convex functionals in Banach spaces,” Zh. Vychisl. Mat. Mat. Fiz., 46, No. 3, 372–378 (2006).

N. Buong, “Convergence rates and finite-dimensional approximation for a class of ill-posed variational inequalities,” Ukr. Math. J., 48, No. 5, 697–707 (1996).

N. Buong, “On ill-posed problems in Banach spaces,” South. Asian Bull. Math., 21, 95–193 (1997).

N. Buong, “Operator equations of Hammerstein type under monotone perturbations,” Proc. NCST Vietnam, 11, No. 2, 3–7 (1999).

N. Buong, “Convergence rates in regularization for the case of monotone perturbations,” Ukr. Math. J., 52, No. 2, 285–293 (2000).

A. S. Antipin, “Solution methods for variational inequalities with coupled constraints,” Comput. Math. Math Phys., 40, No. 9, 1239–1254 (2000).

A. S. Antipin, “Solving variational inequalities with coupling constraints with the use of differential equations,” Different. Equat., 36, No. 11, 1587–1596 (2000).