Duality in Convex Problems of Bolza over Functions of Bounded Variation
Teemu Pennanen, Ari-Pekka Perkkiö · SIAM Journal on Control and Optimization · 2014
This paper studies fully convex problems of Bolza in the conjugate duality framework of Rockafellar. We parameterize the problem by a general Borel measure which has a direct interpretation in certain problems of financial economics. We derive a dual representation for the optimal value function in terms of continuous dual trajectories and we give conditions for the existence of solutions. Combined with well-known results on problems of Bolza over absolutely continuous trajectories, we obtain optimality conditions in terms of extended Hamiltonian equations.