ABSTRACT
This chapter focuses on two main ideas. The first idea is that constrained problems in optimal control theory and the calculus of variations can be reformulated, by using special derivative multipliers, as unconstrained calculus of variations problems. The second idea is that, critical point solutions for the reformulated problem, which include the determination of the multipliers, immediately follow from Euler-Lagrange equations for the unconstrained problem. This critical point solution is a necessary condition for the original constrained problem. This allows us to obtain a true Lagrange multiplier rule where both the original variables and the multipliers can be explicitly and easily determined. The chapter provides a basic reformulation for optimal control problems which includes the bounded state variable case, and gives a reformulation for constrained problems in the calculus of variations. It also provides a second reformulation of these constrained problems which is similar to the classical Kuhn-Tucker reformulation.
