THE ORTHOGONALITY THEOREM AND THE STRONG-F-MONOTONICITY CONDITION FORVARIATIONAL INEQUALITY ALGORITHMS

We introduce an approach, called the orthogonality theorem, for establ ishing the convergence of several algorithms for solving variational i nequalities. This theorem, as well as several basic convergence theore ms from the literature, impose the condition of strong-f-monotonicity on the problem function. We analyze and introduce some new results con cerning this condition and provide a general overview of its propertie s. For example, we show the relationship between strong-f-monotonicity and convexity.