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Acceleration of stochastic approximation by averaging
A new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated. Convergence with probability one is proved for a variety of classical optimization andExpand
Some methods of speeding up the convergence of iteration methods
Abstract For the solution of the functional equation P (x) = 0 (1) (where P is an operator, usually linear, from B into B, and B is a Banach space) iteration methods are generally used. These consistExpand
Cubic regularization of Newton method and its global performance
We provide theoretical analysis for a cubic regularization of Newton method as applied to unconstrained minimization problem. Expand
Minimization of unsmooth functionals
WE consider the minimization of a convex, but but necessarily differentiable, functional in a convex set of Hilbert space. The minimization method amounts to movement along a reference functional.Expand
The conjugate gradient method in extremal problems
Abstract THE conjugate gradient method was first described in [1, 2] for solving sets of linear algebraic equations. The method, being iterative in form, has all the merits of iterative methods, andExpand
The method of projections for finding the common point of convex sets
Abstract MANY mathematical and applied problems can be reduced to finding some common point of a system (finite or infinite) of convex sets. Usually each of the sets is such that it is not difficultExpand
Convexity of Quadratic Transformations and Its Use in Control and Optimization
Quadratic transformations have the hidden convexity property which allows one to deal with them as if they were convex functions. This phenomenon was encountered in various optimization and controlExpand
Multi-Input Multi-Output Ellipsoidal State Bounding
Ellipsoidal state outer bounding has been considered in the literature since the late sixties. As in the Kalman filtering, two basic steps are alternated: a prediction phase, based on theExpand