Abstract
In this paper, new numerical algorithms are introduced for finding the solution of a variational inequality problem whose constraint set is the common elements of the set of fixed points of a demicontractive mapping and the set of solutions of an equilibrium problem for a monotone mapping in a real Hilbert space. The strong convergence of the iterates generated by these algorithms is obtained by combining a viscosity approximation method with an extragradient method. First, this is done when the basic iteration comes directly from the extragradient method, under a Lipschitz-type condition on the equilibrium function. Then, it is shown that this rather strong condition can be omitted when an Armijo-backtracking linesearch is incorporated into the extragradient iteration. The particular case of variational inequality problems is also examined.
Original language | English |
---|---|
Pages (from-to) | 429-451 |
Number of pages | 23 |
Journal | Optimization |
Volume | 64 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Jan 2015 |
Keywords
- Armijo-backtracking linesearch
- demicontractive mapping
- equilibrium problem
- extragradient method
- fixed point problem
- Lipschitz continuity
- viscosity approximation method