Auxiliary principle technique for general harmonic variational inequalities

Abstract

In this Paper, we have introduced and analyzed certain new types of harmonic variational inequalities, such as Auxiliary general Harmonic variational inequalities. The optimality conditions of general harmonic convex functions are shown to be specified by auxiliary general harmonic variational inequalities. Using the harmonic variational inequality, it is demonstrated that the harmonic convex set’s minimum of a differentiable harmonic convex function may be described. In addition to the auxiliary principle technique, other hybrid proximal point methods are proposed. The convergence of the proposed method is shown to depend only on the operator being pseudo-monotonic, which is a weaker criterion than monotonicity. The findings presented in this work may encourage more study in this area.