LINEAR-QUADRATIC PROGRAMMING AND OPTIMAL-CONTROL

A generalized approach is taken to linear and quadratic programming in which dual as well as primal variables may be subjected to bounds, and constraints may be represented through penalties. Corresponding problem models in optimal control related to continuous-time programming are then set up and theorems on duality and the existence of solutions are derived. Optimality conditions are obtained in the form of a global saddle point property which decomposes into an instantaneous saddle point condition on the primal and dual control vectors at each time, along with an endpoint condition.