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Journal ArticleDOI

Generalized Hamiltonian equations for convex problems of Lagrange.

01 May 1970-Pacific Journal of Mathematics (Pacific Journal of Mathematics)-Vol. 33, Iss: 2, pp 411-427
About: This article is published in Pacific Journal of Mathematics.The article was published on 1970-05-01 and is currently open access. It has received 82 citations till now. The article focuses on the topics: Convex analysis & Linear matrix inequality.

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Citations
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TL;DR: In this article, the authors present a set of sufficient conditions on the Hamiltonian for such dynamical systems to converge to a steady state as time tends to infinity, based on the work of Cass and Shell, Rockafellar, and Hartman and Olech.

161 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the problem of minimizing an integral of the form ∫ 0 + ∞ L (k ( t ), k ( t )) e − pt dt is minimized over a class of arcs k : [0, +∞) → R n.

126 citations

References
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TL;DR: In this paper, the conjugates of convex integral functionals on Banach spaces of continuous vector-valued functions were derived for the existence theory and duality theory for various optimization problems, and these formulas imply the weak compactness of certain convex sets of summable functions.
Abstract: Formulas are derived in this paper for the conjugates of convex integral functionals on Banach spaces of measurable or continuous vector-valued functions. These formulas imply the weak compactness of certain convex sets of summable functions, and they thus have applications in the existence theory and duality theory for various optimization problems. They also yield formulas for the subdifferentials of integral functionals, as well as characterizations of supporting hyperplanes and normal cones.

548 citations