Stochastic optimization procedure convergence with Markov switching in the averaging scheme

U.T.Himka; Ya.M.Chabanyuk

We established sufficient conditions for the convergence of the multi-dimensional continuous stochastic optimization procedure in the case of direct dependence of the regression function on the environment, which described by Markov switching. Additional conditions on Lyapunov function of the averaged pure gradient system have been aquired in the assumption of exponential stability for the averaged evolutionary system according to the Markov process stationary distribution.

1. Kiefer~E., Wolfowitz~J. Stochastic estimation of the maximum of regression function// Ann. Math. Statist. -- 1952. -- V.23, №3. -- P. 462--466.

2. Nevelson~M.S., Khasminsky~R.Z. Stochastic Approximation and Recurrence Evaluation. - Nauka, Moscow, 1972. -- 332 p.

3. Чабанюк Я.М. Процедура стохастичної апроксимації в ергодичному середовищі Маркова// Мaт. Студ. -- 2004. -- Т.21, №1. -- С. 81--86.

4. Korolyuk~V.S., Limnios~N. Stochastic Systems in Merging Phase Space. -- World Scientific, Singapore, 2005. -- 330 p.

	Stochastic optimization procedure convergence with Markov switching in the averaging scheme
Author	U.T.Himka, Ya.M.Chabanyuk ulyana.himka@gmail.com Lviv Polytechnic National University
Abstract	We established sufficient conditions for the convergence of the multi-dimensional continuous stochastic optimization procedure in the case of direct dependence of the regression function on the environment, which described by Markov switching. Additional conditions on Lyapunov function of the averaged pure gradient system have been aquired in the assumption of exponential stability for the averaged evolutionary system according to the Markov process stationary distribution.
Keywords	stochastic optimization, Markov process, Lyapunov function, stochastic optimization
DOI	doi:10.30970/ms.34.1.101-105
Reference	1. Kiefer~E., Wolfowitz~J. Stochastic estimation of the maximum of regression function// Ann. Math. Statist. -- 1952. -- V.23, №3. -- P. 462--466. 2. Nevelson~M.S., Khasminsky~R.Z. Stochastic Approximation and Recurrence Evaluation. - Nauka, Moscow, 1972. -- 332 p. 3. Чабанюк Я.М. Процедура стохастичної апроксимації в ергодичному середовищі Маркова// Мaт. Студ. -- 2004. -- Т.21, №1. -- С. 81--86. 4. Korolyuk~V.S., Limnios~N. Stochastic Systems in Merging Phase Space. -- World Scientific, Singapore, 2005. -- 330 p.
Pages	101-105
Volume	34
Issue	1
Year	2010
Journal	Matematychni Studii
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