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In this paper we will study three hypotheses proposed by L. I. Rozonoer(Automation and Remote Control, 2003, vol.64, no.8, pp.1237--1240) in optimalcontrol theory in order to derive conditions for the existence of an optimalcontrol under all initial conditions, and the relationships between Pontryaginmaximum principle and the dynamic programming method.

On Certain Hypotheses in Optimal Control Theory and the Relationship of  the Maximum Principle with the Dynamic Programming Method Proposed by L. I.  Rozonoer