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 and… Expand

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 consist… Expand

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

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, and… Expand

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 difficult… Expand

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 control… Expand

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 the… Expand