Results 301 to 310 of about 6,406,771 (368)
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International Journal of Control, 1974
Abstract This paper presents a relatively simple proof of the maximum principle. The main objective has been to obtain a proof, similar to that due to Halkin, but replacing the use of Brouwer's fixed point theorem by an easily proven contraction mapping theorem.
David Q. Mayne, G. F. Bryant
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Abstract This paper presents a relatively simple proof of the maximum principle. The main objective has been to obtain a proof, similar to that due to Halkin, but replacing the use of Brouwer's fixed point theorem by an easily proven contraction mapping theorem.
David Q. Mayne, G. F. Bryant
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Numerical Methods for Partial Differential Equations, 2019
In this paper, we present two types of unconditionally maximum principle preserving finite element schemes to the standard and conservative surface Allen–Cahn equations. The surface finite element method is applied to the spatial discretization.
Xufeng Xiao, Ruijian He, Xinlong Feng
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In this paper, we present two types of unconditionally maximum principle preserving finite element schemes to the standard and conservative surface Allen–Cahn equations. The surface finite element method is applied to the spatial discretization.
Xufeng Xiao, Ruijian He, Xinlong Feng
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1972
The values that an analytic function assumes in the different parts of its domain of existence are related to each other : they are connected by analytic continuation and it is impossible to modify the values in one part without inducing a change throughout.
Gabor Szegö, George Pólya
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The values that an analytic function assumes in the different parts of its domain of existence are related to each other : they are connected by analytic continuation and it is impossible to modify the values in one part without inducing a change throughout.
Gabor Szegö, George Pólya
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Mathematische Operationsforschung und Statistik. Series Optimization, 1979
A model of optimal control for discrete systems and the historical development of the discrete maximum principle are considered. The paper deals with local optimality conditions of the first order, e.g. with a local maximum-principle and a quasi-maximum principle. Furthermore, optimality conditions of higher order, e. g.
R. Gabasov, F. M. Kirillova
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A model of optimal control for discrete systems and the historical development of the discrete maximum principle are considered. The paper deals with local optimality conditions of the first order, e.g. with a local maximum-principle and a quasi-maximum principle. Furthermore, optimality conditions of higher order, e. g.
R. Gabasov, F. M. Kirillova
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1996
In practical problems certain essential constraints are usually imposed on the control set. For such problems the necessary conditions for optimal control stated in the preceding chapter are, in general, not suitable. Necessary conditions for optimality in such problems are furnished by Pontryagin’s maximum principle, which is the subject of this ...
V. B. Kolmanovskii +2 more
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In practical problems certain essential constraints are usually imposed on the control set. For such problems the necessary conditions for optimal control stated in the preceding chapter are, in general, not suitable. Necessary conditions for optimality in such problems are furnished by Pontryagin’s maximum principle, which is the subject of this ...
V. B. Kolmanovskii +2 more
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The Pontryagin Maximum Principle in the Wasserstein Space
Calculus of Variations and Partial Differential Equations, 2017We prove a Pontryagin Maximum Principle for optimal control problems in the space of probability measures, where the dynamics is given by a transport equation with non-local velocity. We formulate this first-order optimality condition using the formalism
Benoît Bonnet, Francesco Rossi
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Discrete maximum principle [PDF]
Mathematical Notes of the Academy of Sciences of the USSR, 1983 The general method of subdifferentiation developed in the author's previous paper [Sov. Math., Dokl. 23, 367-371 (1981; Zbl 0474.46002)] is applied for the derivation of necessary optimality conditions in a finite-step dynamical problem with nonsmooth data and with a vector- valued criteria.
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Nonlinear Analysis: Theory, Methods & Applications, 1997
In optimal control problems, where the operator describing the dynamics of the process and the terminal condition is not regular, that is, its first Fréchet derivative is not surjective at the optimal process, the fundamental first-order necessary conditions offered by the Pontryagin maximum principle do not provide useful and sufficient information ...
Urszula Ledzewicz, Heinz Schättler
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In optimal control problems, where the operator describing the dynamics of the process and the terminal condition is not regular, that is, its first Fréchet derivative is not surjective at the optimal process, the fundamental first-order necessary conditions offered by the Pontryagin maximum principle do not provide useful and sufficient information ...
Urszula Ledzewicz, Heinz Schättler
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Discovery of the Maximum Principle
Journal of Dynamical and Control Systems, 1999A short history of the discovery of the maximum principle in optimal control theory, in the mid fifties, by L. S. Pontryagin and his associates is presented. There are pointed out the most important steps and individual contributions by the members of the group towards the final form of that it is known as maximum principle.
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Maximum principles in analytical economics [PDF]
Synthese, 1971 The very name of my subject, economics, suggests economizing or maxi mizing. But Political Economy has gone a long way beyond home econo mics. Indeed, it is only in the last third of the century, within my own life time as a scholar, that economic theory has had many pretensions to being itself useful to the practical businessman or bureaucrat.
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