The general theory of relaxation processes for convex functionals

This article sets out a theory of the convergence of minimization processes convex functionals that reduce the value of the functional at each step. A geometrical language, independent of the algorithmic structure, is used to describe the processes: the language of relaxation angles and factors. Convergence conditions are derived and the rate of convergence and stability of the process are studied in this terminology. Translation from the language of concrete algorithms to the geometrical terminology is not difficult, and thanks to this the theory has a wide area of applications: gradient and operator-gradient processes, processes of Newtonian type, coordinate relaxation, Jacobi processes and relaxation for the Rayleigh functional.