Duality in convex problems of Bolza over functions of bounded variation

Teemu Pennanen; Ari-Pekka Perkkiö

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arXiv · 1309.2121

Duality in convex problems of Bolza over functions of bounded variation

Teemu Pennanen·Ari-Pekka Perkkiö

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Abstract

This paper studies convex problems of Bolza in the conjugate duality framework of Rockafellar. We parameterize the problem by a general Borel measure which has direct economic interpretation in problems of financial economics. We derive a dual representation for the optimal value function in terms of continuous dual arcs and we give conditions for the existence of solutions. Combined with well-known results on problems of Bolza over absolutely continuous arcs, we obtain optimality conditions in terms of extended Hamiltonian conditions.

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Teemu Pennanen, Ari-Pekka Perkkiö. 2013-09-09. Duality in convex problems of Bolza over functions of bounded variation. https://arxiv.org/abs/1309.2121

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