Self-dual approximations to fully convex impulsive systems

Fully convex optimal control problems contain a Lagrangian that is jointly convex in the state and velocity variables. Problems of this kind have been widely investigated by Rockafellar and collaborators if the Lagrangian is coercive and without state constraints. A lack of coercivity implies the dual has nontrivial state constraints, and vice versa (that is, they are dual concepts in convex analysis). We consider a framework using Goebel's self-dualizing technique that approximates both the primal and dual problem simultaneously and maintains the duality relationship. Previous results are applicable to the approximations, and we investigate the limiting behavior as the approximations approach the original problem. A specific example is worked out in detail.