Results 281 to 290 of about 4,636,575 (354)

The maximum principle

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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Unconditionally maximum principle preserving finite element schemes for the surface Allen–Cahn type equations

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
semanticscholar   +1 more source

Discovery of the Maximum Principle

Journal of Dynamical and Control Systems, 1999
A 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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On the Stochastic Maximum Principle

SIAM Journal on Control and Optimization, 1978
A 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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A Stochastic Maximum Principle

SIAM Journal on Control and Optimization, 1976
The 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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Aleksandrov maximum principle and bony maximum principle for parabolic equations

Acta Mathematicae Applicatae Sinica, 1985
The author simplifies the proof of the Aleksandrov maximum principle for parabolic equations given by Krylov and obtains finer results. He further proves the Bony maximum principle for parabolic equations by using the above results.
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The Pontryagin Maximum Principle in the Wasserstein Space

Calculus of Variations and Partial Differential Equations, 2017
We 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
semanticscholar   +1 more source

The maximum principle

1996
Our study thus far points to the maximum principle as the fundamental principle of optimality and identifies the symplectic structure and the associated Hamiltonian formalism as the main theoretical ingredients required for its proper understanding. In this chapter we shall take that direction to its natural end and ultimately arrive at a geometric ...
V. N. Afanas’ev, V. B. Kolmanovskii, V. R. Nosov   +2 more
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A maximum principle for mean-field stochastic control system with noisy observation

at - Automatisierungstechnik, 2022
Guangchen Wang, Zhanghua Wu
semanticscholar   +1 more source

The Maximum Principle

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.
George Pólya, Gabor Szegö
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