On Duality and the Maximum Principle for Continuous Linear Programming Problems

Abstract

In this paper, the Grinold maximum principle for continuous linear programming problems is extended to the case where the known duality theorems do not ensure the existence of an optimal solution of the dual problem in the usual reflexive $L_p$-spaces. The extended maximum principle is then applied to the investigation of a parabolic boundary control proble in with constraints on the control and the state.