All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 56 Next

Displaying 1101 – 1120 of 2377

Showing per page

Mean-Field Optimal Control

Massimo Fornasier, Francesco Solombrino (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We introduce the concept of mean-field optimal control which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents. While in the classical mean-field theory one studies the behavior of a large number of small individuals freely interacting...

Measure solutions for semilinear evolution equations with polynomial growth and their optimal control

N.U. Ahmed (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.

Measure valued solutions for systems governed by neutral differential equations on Banach spaces and their optimal control

N.U. Ahmed (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider the question of existence of measure valued solutions for neutral differential equations on Banach spaces when there is no mild solutions. We prove the existence of measure solutions and their regularity properties. We consider also control problems of such systems and prove existence of optimal feedback controls for some interesting a-typical control problems.

Méthodes de réalisation de produit scalaire et de problème de moments avec maximisation d'entropie

Valerie Girardin (1997)

Studia Mathematica

We develop several methods of realization of scalar product and generalized moment problems. Constructions are made by use of a Hilbertian method or a fixed point method. The constructed solutions are rational fractions and exponentials of polynomials. They are connected to entropy maximization. We give the general form of the maximizing solution. We show how it is deduced from the maximizing solution of the algebraic moment problem.

Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet

Bernard Bonnard, Monique Chyba (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Consider a sub-riemannian geometry(U,D,g) where U is a neighborhood of 0 in R3, D is a Martinet type distribution identified to ker ω, ω being the 1-form: ω = d z - y 2 2 d x , q=(x,y,z) and g is a metric on D which can be taken in the normal form: g = a ( q ) d x 2 + c ( q ) d y 2 , a=1+yF(q), c=1+G(q), G | x = y = 0 = 0 . In a previous article we analyze the flat case: a=c=1; we describe the conjugate and cut loci, the sphere and the wave front. The objectif of this article is to provide a geometric and computational framework to analyze the general case....

Metric subregularity for nonclosed convex multifunctions in normed spaces

Xi Yin Zheng, Kung Fu Ng (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In terms of the normal cone and the coderivative, we provide some necessary and/or sufficient conditions of metric subregularity for (not necessarily closed) convex multifunctions in normed spaces. As applications, we present some error bound results for (not necessarily lower semicontinuous) convex functions on normed spaces. These results improve and extend some existing error bound results.

Metric subregularity of order q and the solving of inclusions

Michaël Gaydu, Michel Geoffroy, Célia Jean-Alexis (2011)

Open Mathematics

We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Hölder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.

Michael's theorem for Lipschitz cells in o-minimal structures

Małgorzata Czapla, Wiesław Pawłucki (2016)

Annales Polonici Mathematici

A version of Michael's theorem for multivalued mappings definable in o-minimal structures with M-Lipschitz cell values (M a common constant) is proven. Uniform equi-LCⁿ property for such families of cells is checked. An example is given showing that the assumption about the common Lipschitz constant cannot be omitted.

Currently displaying 1101 – 1120 of 2377