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Maximum principles for second order dynamic equations on time scales
Journal of Mathematical Analysis and Applications, 2007 This paper establishes some: new maximum principles for second order dynamic equations on time scales, including: a strong maximum principle; a generalized maximum principle; and a boundary point lemma.
Petr Stehlik
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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.
Gabasov, R., Kirillova, F.
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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.
Gabasov, R., Kirillova, F.
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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 ...
Ledzewicz, Urszula, Schättler, Heinz
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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 ...
Ledzewicz, Urszula, Schättler, Heinz
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Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2014 In this paper, we establish extended maximum principles for solutions to linear parabolic partial differential inequalities on unbounded domains, where the solutions satisfy a variety of growth/decay conditions on the unbounded domain.
J C Meyer, D J Needham
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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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Computational Methods in Applied Mathematics, 2012
Abstract A singularly perturbed convection-diffusion problem is considered. In certain circumstances the solution is shown to be much smaller than its maximum outside a neighborhood of a subcharacteristic curve.
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Abstract A singularly perturbed convection-diffusion problem is considered. In certain circumstances the solution is shown to be much smaller than its maximum outside a neighborhood of a subcharacteristic curve.
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A Stochastic Maximum Principle
SIAM Journal on Control and Optimization, 1976The major theorem of this paper is very closely parallel to the classical Pontryagin maximum principle. The classical case, very roughly stated, says that if $u(t)$ is a control function which has an associated trajectory $x(t)$, then there is a function $H(v,x,t)$ such that $u(t)$ is optimal only if for each t and for all v in the control set, \[H(u(t)
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On the Stochastic Maximum Principle
SIAM Journal on Control and Optimization, 1978A representation of the adjoint process, which appears in a general version of the maximum principle for control systems described by Girsanov solutions of stochastic differential equations, is given in terms of the linearization of the state equation.
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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.
G. F. BRYANT, D. Q. MAYNE
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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.
G. F. BRYANT, D. Q. MAYNE
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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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