Duality in convex problems of Bolza over functions of bounded variation

TY - JOUR

T1 - Duality in convex problems of Bolza over functions of bounded variation

AU - Pennanen, Teemu

AU - Perkkiö, Ari-Pekka

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

U2 - 10.1137/130917612

DO - 10.1137/130917612

M3 - Article

SN - 0363-0129

VL - 52

SP - 1481

EP - 1498

JO - SIAM JOURNAL ON CONTROL AND OPTIMIZATION

JF - SIAM JOURNAL ON CONTROL AND OPTIMIZATION

IS - 3

ER -