The Sakawa-Shindo Algorithm in Stochastic Control

JUSTINA GIANATTI; JOSEPH FRÉDÉRIC BONNANS; FRANCISCO A. SILVA

Paris

Conferencia; SIAM Conference of Control and its Applications; 2015

INRIA

We study the extension to the stochastic caseof a first order algorithm for solving deterministic optimalcontrol problems proposed by Y. Sakawa and Y. Shindo.On global convergence of an algorithm for optimal control.IEEE Trans Aut. Control. vAC-25. 1149, 1980, and analyzedin J.F. Bonnans. On an algorithm for optimal controlusing Pontryagin?s maximum principle. SIAM J. Controland Optimization, 24, 1986. We need to assume that eitherthe cost functional is Lipschitz and the volatility term isnot controlled, or that the dynamics is an affine function ofthe state and the control. We prove that the iterates of thealgorithm are well defined and the cost function decreases.Moreover, for convex problems we obtain the convergenceof the iterates in the weak topology.