Duality in Convex Problems of Bolza over Functions of Bounded Variation

Pennanen, Teemu und Perkkiö, Ari-Pekka (2014): Duality in Convex Problems of Bolza over Functions of Bounded Variation. In: SIAM Journal on Control and Optimization, Bd. 52, Nr. 3: S. 1481-1498

Abstract

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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Finanz- und Versicherungsmathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0363-0129
• Sprache: Englisch