Modified projected subgradient method for solving pseudomonotone equilibrium and fixed point problems in Banach spaces. (English) Zbl 1476.65117
Summary: Motivated by the work of D. Van Hieu and J. J. Strodiot [J. Fixed Point Theory Appl. 20, No. 3, Paper No. 131, 32 p. (2018; Zbl 1401.90238)], we introduce a new projected subgradient method for solving pseudomonotone equilibrium and fixed point problem in Banach spaces. The main iterative steps in the proposed method use a projection method and do not require any Lipschitz-like condition on the equilibrium bifunction. A strong convergence result is proved under mild conditions and we applied our algorithm to solving pseudomonotone variational inequalities in Banach spaces. Also, we provide some numerical examples to illustrate the performance of the proposed method and compare it with other methods in the literature.
MSC:
| 65K15 | Numerical methods for variational inequalities and related problems |
| 47J25 | Iterative procedures involving nonlinear operators |
| 65J15 | Numerical solutions to equations with nonlinear operators |
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
Keywords:
equilibrium problem; pseudomonotone; phi-quasi-Fejer monotone; projection method; extragradient method; Banach spacesCitations:
Zbl 1401.90238References:
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