On the method of generalized stochastic gradients and quasi-Féjer sequences

Research paper by Yu. M. Ermol'ev

Indexed on: 01 Mar '69Published on: 01 Mar '69Published in: Cybernetics and Systems Analysis


It is of particular importance to find new means, different from (13)–(14), of controlling the step length ϱ s. Apart from the fact that the control (13)–(14) has a rigid, programmed nature, it is determinate, i.e., it does not depend on the actual trajectory of the “descent.” The process (9)–(10) is random and defines a whole family of trajectories from the initial point to the minimum point. The control (13)–(14) is calculated once for the whole family, so sufficiently rapid convergence cannot be expected from it. For a stochastic method of the form (9)–(10), stochastic means of control (see [17]) depending on the previous history of the “descent” are more natural.