Generalized D-gap functions for hemivariational inequalities in Hilbert spaces

In this paper, we are committed to the study of generalized difference gap (D-gap) functions and error bounds for hemivariational inequalities in Hilbert spaces. By introducing a new gap function, we define a generalized D-gap function for the hemivariational inequality considered, for which we investigate the local Lipschitz continuity and coercivity. Then, some error bound results for the generalized D-gap function are established and the relationship between the solution to the hemivariational inequality and the stationary point of the generalized D-gap function is discussed. Finally, we construct a descent algorithm for solving the hemivariational inequality based on the generalized D-gap function and further prove a convergence result for the algorithm.