The Orthogonality Theorem and the Strong-f-Monotonicity Condition for Variational Inequality Algorithms

We introduce an approach, called the orthogonality theorem, for establishing the convergence of several algorithms for solving variational inequalities. This theorem, as well as several basic convergence theorems from the literature, impose the condition of strong-f-monotonicity on the problem function. We analyze and introduce some new results concerning this condition and provide a general overview of its properties. For example, we show the relationship between strong-f-monotonicity and convexity.