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P. Halmos (1956)
Lectures on ergodic theory
J. Peetre, G. Sparr (1972)
Interpolation of normed abelian groupsAnnali di Matematica Pura ed Applicata, 92
Differential Equations, Vol. 39, No. 12, 2003, pp. 1671–1679. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 12, 2003, pp. 1587–1595. Original Russian Text Copyright c 2003 by Arutyunov. ORDINARY DIFFERENTIAL EQUATIONS The Pontryagin Maximum Principle and Sucient Optimality Conditions for Nonlinear Problems A. V. Arutyunov Friendship of Nations University, Moscow, Russia Received June 10, 2003 The Pontryagin maximum principle is a rst-order necessary condition for a minimum in optimal control problems described by ordinary di erential equations [1]. However, the question arises as what type of minimum corresponds to this necessary condition. Indeed, the classical calculus of variations traditionally deals with two types of minimum, strong and weak. At the same time, in the classical monograph [1], the founders of optimal control theory studied a global minimum (i.e., assumed that the value of the functional to be minimized on the control in question does not exceed the value on any admissible control). Hence they solved the main problem (i.e., proved the Pontryagin maximum principle in the general nonlinear case) without clarifying the type of minimum (weaker than global) to which the maximum principle corresponds. We answer this question in the present paper. To this end, we introduce an appropriate
Differential Equations – Springer Journals
Published: Oct 5, 2004
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