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Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group

Yves Achdou, Italo Capuzzo-Dolcetta (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and analyze numerical schemes for viscosity solutions of time-dependent Hamilton-Jacobi equations on the Heisenberg group. The main idea is to construct a grid compatible with the noncommutative group geometry. Under suitable assumptions on the data, the Hamiltonian and the parameters for the discrete first order scheme, we prove that the error between the viscosity solution computed at the grid nodes and the solution of the discrete problem behaves like h where h is the mesh step. Such...

Approximation of the pareto optimal set for multiobjective optimal control problems using viability kernels

Alexis Guigue (2014)

ESAIM: Control, Optimisation and Calculus of Variations

This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solution of...

Approximation of the Snell envelope and american options prices in dimension one

Vlad Bally, Bruno Saussereau (2002)

ESAIM: Probability and Statistics

We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.

Approximation of the Snell Envelope and American Options Prices in dimension one

Vlad Bally, Bruno Saussereau (2010)

ESAIM: Probability and Statistics

We establish some error estimates for the approximation of an optimal stopping problem along the paths of the Black–Scholes model. This approximation is based on a tree method. Moreover, we give a global approximation result for the related obstacle problem.

Approximations by regular sets and Wiener solutions in metric spaces

Anders Björn, Jana Björn (2007)

Commentationes Mathematicae Universitatis Carolinae

Let X be a complete metric space equipped with a doubling Borel measure supporting a weak Poincaré inequality. We show that open subsets of X can be approximated by regular sets. This has applications in nonlinear potential theory on metric spaces. In particular it makes it possible to define Wiener solutions of the Dirichlet problem for p -harmonic functions and to show that they coincide with three other notions of generalized solutions.

Approximations of parabolic variational inequalities

Alexander Ženíšek (1985)

Aplikace matematiky

The paper deals with an initial problem of a parabolic variational inequality whichcontains a nonlinear elliptic form a ( v , w ) having a potential J ( v ) , which is twice G -differentiable at arbitrary v ∈ H 1 ( Ω ) . This property of a ( v , w ) makes it possible to prove convergence of an approximate solution defined by a linearized scheme which is fully discretized - in space by the finite elements method and in time by a one-step finite-difference method. Strong convergence of the approximate solution is proved without any regularity...

A-Quasiconvexity: Relaxation and Homogenization

Andrea Braides, Irene Fonseca, Giovanni Leoni (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Integral representation of relaxed energies and of Γ-limits of functionals ( u , v ) ↦ ∫ Ω f ( x , u ( x ) , v ( x ) ) d x are obtained when sequences of fields v may develop oscillations and are constrained to satisfy a system of first order linear partial differential equations. This framework includes the treatement of divergence-free fields, Maxwell's equations in micromagnetics, and curl-free fields. In the latter case classical relaxation theorems in W1,p, are recovered.

Arrow-type sufficient conditions for optimality of age-structured control problems

Vladimir Krastev (2013)

Open Mathematics

We consider a class of age-structured control problems with nonlocal dynamics and boundary conditions. For these problems we suggest Arrow-type sufficient conditions for optimality of problems defined on finite as well as infinite time intervals. We examine some models as illustrations (optimal education and optimal offence control problems).

Asignación de recursos Max-Min: propiedades y algoritmos.

Amparo Mármol Conde, Blas Pelegrín Pelegrín (1991)

Trabajos de Investigación Operativa

Este trabajo trata el problema de asignación de recursos cuando el objetivo es maximizar la mínima recompensa y las funciones recompensa son continuas y estrictamente crecientes. Se estudian diferentes propiedades que conducen a algoritmos que permiten de forma eficiente la resolución de gran variedad de problemas de esta naturaleza, tanto con variables continuas como discretas.

Currently displaying 641 – 660 of 4405