Gradient methods with memory

In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at previous iterations in order to accelerate convergence towards optimal solution. This is used form of a piece-wise linear model objective function, provides us with much better prediction abilities as compared standard model. To best our knowledge, approach was never really applied Convex Minimization differentiable functions view high complexity corresponding auxiliary problems. However, show that all necessary computations can be done very efficiently. Consequently, get new optimization methods, are than usual Gradient Methods both number oracle calls and computational time. Our theoretical conclusions confirmed by preliminary experiments.