Results 301 to 310 of about 6,692,173 (358)
Some of the next articles are maybe not open access.
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
openaire +2 more sources
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
openaire +2 more sources
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
openaire +2 more sources
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
openaire +2 more sources
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
openaire +3 more sources
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
openaire +3 more sources
Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions
Calculus of Variations and Partial Differential Equations, 2016In this paper, we consider equations involving fully nonlinear non-local operators Fα(u(x))≡Cn,αPV∫RnG(u(x)-u(z))|x-z|n+αdz=f(x,u).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb ...
Wenxiong Chen, Congming Li, Guanfeng Li
semanticscholar +1 more source
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
openaire +4 more sources
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
openaire +4 more sources
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.
openaire +2 more sources
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
openaire +2 more sources
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
openaire +2 more sources
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.
openaire +3 more sources
1998
The strong maximum principle of E. Hopf says that a solution of an elliptic PDE cannot assume an interior maximum. This leads to further results about solutions of such PDEs, like removability of singularities, gradient bounds, or Liouville’s theorem saying that every bounded harmonic functions defined on all of Euclidean space is constant.
openaire +2 more sources
The strong maximum principle of E. Hopf says that a solution of an elliptic PDE cannot assume an interior maximum. This leads to further results about solutions of such PDEs, like removability of singularities, gradient bounds, or Liouville’s theorem saying that every bounded harmonic functions defined on all of Euclidean space is constant.
openaire +2 more sources
2014
The stochastic maximum principle (SMP) gives some necessary conditions for optimality for a stochastic optimal control problem. We give a summary of well-known results concerning stochastic maximum principle in finite-dimensional state space as well as some recent developments in infinite-dimensional state space.
openaire +3 more sources
The stochastic maximum principle (SMP) gives some necessary conditions for optimality for a stochastic optimal control problem. We give a summary of well-known results concerning stochastic maximum principle in finite-dimensional state space as well as some recent developments in infinite-dimensional state space.
openaire +3 more sources