The linear programming approach to deterministic optimal control problems Daniel Hernández-Hernández; Onésimo Hernández-Lerma; Michael Taksar — 1996 Applicationes Mathematicae Given a deterministic optimal control problem (OCP) with value function, say J * , we introduce a linear program ( P ) and its dual ( P * ) whose values satisfy sup ( P * ) ≤ inf ( P ) ≤ J * ( t , x ) . Then we give conditions under which (i) there is no duality gap