##
**Merit functions and equivalent differentiable optimization problems for the extended general variational inequalities.**
*(English)*
Zbl 1213.90233

Summary: We study some merit functions and equivalent differentiable optimization problems for the extended general variational inequalities involving three operators, which was introduced and studied by M. A. Noor [Projection iterative methods for extended general variational inequalities, J. Appl. Math. Comput. 32, No. 1, 83–95 (2009)] very recently. Using the projection technique, we obtain some error bounds for the solution of extended general variational inequalities under some mild conditions, and then formulate the extended general variational inequalities as differentiable constrained (or unconstrained) optimization problems. We also prove that the extended general variational inequalities have a unique solution under some conditions.

### MSC:

90C30 | Nonlinear programming |

90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |