Results 231 to 240 of about 5,329,290 (309)

The Maximum Principle

2001
We present here the most significant results which are customarily grouped under the name of Maximum Principle. It supplies a set of necessary conditions of optimality for a wide class of optimal control problems. Firstly, we give a formal, yet synthetic, description of these problems is given.
A. Locatelli
openaire   +2 more sources

The insulated conductivity problem, effective gradient estimates and the maximum principle

Mathematische Annalen, 2021
We consider the insulated conductivity problem with two unit balls as insulating inclusions, a distance of order $$\varepsilon $$ ε apart. The solution u represents the electric potential. In dimensions $$n \ge 3$$ n ≥ 3 it is an open problem to find the
B. Weinkove
semanticscholar   +1 more source

Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation

, 2021
Whether high order temporal integrators can preserve the maximum principle of Allen-Cahn equation has been an open problem in recent years. This work provides a positive answer by designing and analyzing a class of up to fourth order maximum principle ...
Hong Zhang, Jingye Yan, Xu Qian, Songhe Song   +3 more
semanticscholar   +1 more source

On Discrete Maximum Principle

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.
openaire   +2 more sources

AN EXTENDED MAXIMUM PRINCIPLE

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
openaire   +1 more source

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.
openaire   +3 more sources

A nonsmooth maximum principle for a controlled nonconvex sweeping process

, 2020
For an optimal control problem governed by a controlled nonconvex sweeping process, we provide, using an exponential penalization technique, existence of solution and nonsmooth necessary conditions in the form of the Pontryagin maximum principle.
V. Zeidan, Chadi Nour, Hassan Saoud
semanticscholar   +1 more source

A Localized Maximum Principle

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.
openaire   +1 more source

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)
openaire   +1 more source