Inexact model: a framework for optimization and variational inequalities

In this paper, we propose a general algorithmic framework for the first-order methods in optimization broad sense, including minimization problems, saddle-point problems and variational inequalities (VIs). This allows obtaining many known as special case, list accelerated gradient method, composite methods, level-set Bregman proximal methods. The idea of is based on constructing an inexact model main problem component, i.e. objective function or operator VIs. Besides reproducing results, our new which illustrate by universal conditional method VIs with structure. works smooth non-smooth optimal complexity without priori knowledge problem's smoothness. As particular case framework, introduce relative smoothness operators algorithm such operators. We also generalize relatively strongly convex objectives monotone