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Solutions of the Yang-Baxter matrix equation for an idempotent
Weak and strong convergence of prox-penalization and splitting algorithms for bilevel equilibrium problems
1. | Cadi Ayyad University, Faculty of Sciences Semlalia, Mathematics, 40000 Marrakech, Morocco, Morocco |
References:
[1] |
H. Attouch, M. O. Czarnecki and J. Peypouquet, Prox-penalization and splitting methods for constrained variational problems, SIAM J. Control Optim., 21 (2011), 149-173.
doi: 10.1137/100789464. |
[2] |
J. P. Aubin, "Optima and Equilibria: An Introduction to Nonlinear Analysis," Springer, 2nd edition, 2002. |
[3] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145. |
[4] |
O. Chadli, Z. Chbani and H. Riahi, Equilibrium problems with generalized monotone Bifunctions and Applications to Variational inequalities, J. Optim. Theory Appl., 105 (2000), 299-323.
doi: 10.1023/A:1004657817758. |
[5] |
Z. Chbani and H. Riahi, Variational principle for monotone and maximal bifunctions, Serdica Math. J., 29 (2003), 159-166. |
[6] |
N. Hadjisavvas and H. Khatibzadeh, Maximal monotonicity of bifunctions, Optimization, 59 (2010), 147-160.
doi: 10.1080/02331930801951116. |
[7] |
P. E. Mainge and A. Moudafi, Strong convergence of an iterative method for hierarchical fixed-points problems, Pacific J. Optim., 3 (2007), 529-538. |
[8] |
A. Moudafi, Proximal point algorithm extended for equilibrium problems, J. Nat. Geom., 15 (1999), 91-100. |
[9] |
A. Moudafi, On the convergence of splitting proximal methods for equilibrium problems in Hilbert spaces, J. Math Anal. Appl., 359 (2009), 508-513.
doi: 10.1016/j.jmaa.2009.06.005. |
[10] |
A. Moudafi, Proximal methods for a class of bilevel monotone equilibrium problems, J. Global Optimization, 47 (2010), 287-292.
doi: 10.1007/s10898-009-9476-1. |
[11] |
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Aust. Math. Soc., 73 (1967), 591-597.
doi: 10.1090/S0002-9904-1967-11761-0. |
[12] |
G. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl., 72 (1979), 383-390.
doi: 10.1016/0022-247X(79)90234-8. |
show all references
References:
[1] |
H. Attouch, M. O. Czarnecki and J. Peypouquet, Prox-penalization and splitting methods for constrained variational problems, SIAM J. Control Optim., 21 (2011), 149-173.
doi: 10.1137/100789464. |
[2] |
J. P. Aubin, "Optima and Equilibria: An Introduction to Nonlinear Analysis," Springer, 2nd edition, 2002. |
[3] |
E. Blum and W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145. |
[4] |
O. Chadli, Z. Chbani and H. Riahi, Equilibrium problems with generalized monotone Bifunctions and Applications to Variational inequalities, J. Optim. Theory Appl., 105 (2000), 299-323.
doi: 10.1023/A:1004657817758. |
[5] |
Z. Chbani and H. Riahi, Variational principle for monotone and maximal bifunctions, Serdica Math. J., 29 (2003), 159-166. |
[6] |
N. Hadjisavvas and H. Khatibzadeh, Maximal monotonicity of bifunctions, Optimization, 59 (2010), 147-160.
doi: 10.1080/02331930801951116. |
[7] |
P. E. Mainge and A. Moudafi, Strong convergence of an iterative method for hierarchical fixed-points problems, Pacific J. Optim., 3 (2007), 529-538. |
[8] |
A. Moudafi, Proximal point algorithm extended for equilibrium problems, J. Nat. Geom., 15 (1999), 91-100. |
[9] |
A. Moudafi, On the convergence of splitting proximal methods for equilibrium problems in Hilbert spaces, J. Math Anal. Appl., 359 (2009), 508-513.
doi: 10.1016/j.jmaa.2009.06.005. |
[10] |
A. Moudafi, Proximal methods for a class of bilevel monotone equilibrium problems, J. Global Optimization, 47 (2010), 287-292.
doi: 10.1007/s10898-009-9476-1. |
[11] |
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Aust. Math. Soc., 73 (1967), 591-597.
doi: 10.1090/S0002-9904-1967-11761-0. |
[12] |
G. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl., 72 (1979), 383-390.
doi: 10.1016/0022-247X(79)90234-8. |
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