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Convex Programs on Finsler Manifolds

In: New Developments in Differential Geometry, Budapest 1996

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  • Constantin Udriste

    (University POLITEHNICA of Bucharest, Department of Mathematics)

Abstract

Generally a metric structure (Euclidean, Riemannian, Finslerian, Lagrangian, Hamiltonian and their generalizations) suitable selected on a given manifold produces convexity of sets and of real functions via geodesies, but till now were studied intesively only the cases of the Euclidean and Riemannian metrics ([6], [11] and the references). Though basic ideas in the Finslerian convexity were presented by the author in [11], [15], this type of convexity has still a lot of open problems. That’s way the present paper refers again to the convex functions on a Finsler manifold (§2), adding theory of the convex programs (§3), the theory of dual programs (§4), and the Kuhn-Tucker theorem (§5). Basic properties of convex programs on a Riemannian manifold, carry over to the case of a Finsler manifold, if we look the Finsler geometry as a Riemannian geometry without quadratic restriction. Lagrangian, Hamiltonian, and others convexities were not studied at all.

Suggested Citation

  • Constantin Udriste, 1999. "Convex Programs on Finsler Manifolds," Springer Books, in: J. Szenthe (ed.), New Developments in Differential Geometry, Budapest 1996, pages 443-457, Springer.
    • Handle: RePEc:spr:sprchp:978-94-011-5276-1_32
    DOI: 10.1007/978-94-011-5276-1_32
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