Some remarks concerning duality for continuous-time programming problems
Several researchers have studied duality in continuous-time programming. In earlier works there have been problems in duality theorems with the representation of dual variables. In the spaces previously used, very strong conditions have been imposed on the problem to ensure the existence of dual variables. In the simple counterexample of Grinold in continuous-time linear programming the primal problem has an optimal solution and feasible dual solutions but no optimal dual solution. This paper proposes that in the dual problem Lebesgue-Stieltjes integration should be employed in place of Lebesgue integration. In this way the authors are able to obtain results analogous to classical linear and nonlinear duality theory. They also can help in explaining enigmas caused by such problems of Grinold's counterexample.
scientific article; zbMATH DE number 3976815
scientific article