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On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel, Fredi Tröltzsch (2009)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and...

On regularization methods for the numerical solution of parabolic control problems with pointwise state constraints

Ira Neitzel, Fredi Tröltzsch (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study Lavrentiev-type regularization concepts for linear-quadratic parabolic control problems with pointwise state constraints. In the first part, we apply classical Lavrentiev regularization to a problem with distributed control, whereas in the second part, a Lavrentiev-type regularization method based on the adjoint operator is applied to boundary control problems with state constraints in the whole domain. The analysis for both classes of control problems is investigated and...

On second order Hamiltonian systems

Dana Smetanová (2006)

Archivum Mathematicum

The aim of the paper is to announce some recent results concerning Hamiltonian theory. The case of second order Euler–Lagrange form non-affine in the second derivatives is studied. Its related second order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler–Lagrange equations are found.

On some optimal control problems for the heat radiative transfer equation

Sandro Manservisi, Knut Heusermann (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with some optimal control problems for the Stefan-Boltzmann radiative transfer equation. The objective of the optimisation is to obtain a desired temperature profile on part of the domain by controlling the source or the shape of the domain. We present two problems with the same objective functional: an optimal control problem for the intensity and the position of the heat sources and an optimal shape design problem where the top surface is sought as control. The problems...

On the alpine ski with dry friction and air resistance. Some optimization problems for it

Aldo Bressan (1999)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the present work, divided in three parts, one considers a real skis-skier system, Σ R , descending along a straight-line l with constant dry friction; and one schematizes it by a holonomic system Σ = A ∪ U , having any number n ≥ 4 of degrees of freedom and subjected to (non-ideal) constraints, partly one-sided. Thus, e.g., jumps and also «steps made with sliding skis» can be schematized by Σ . Among the n Lagrangian coordinates for Σ two are the Cartesian coordinates ξ and η of its center of mass, C , relative...

On the continuity of minimizers for quasilinear functionals

David Cruz-Uribe, Patrizia Di Gironimo, Luigi D'Onofrio (2012)

Czechoslovak Mathematical Journal

In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by log log ( 1 / | x | ) - 1 . Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann....

On the duality between p -modulus and probability measures

Luigi Ambrosio, Simone Di Marino, Giuseppe Savaré (2015)

Journal of the European Mathematical Society

Motivated by recent developments on calculus in metric measure spaces ( X , d , m ) , we prove a general duality principle between Fuglede’s notion [15] of p -modulus for families of finite Borel measures in ( X , d ) and probability measures with barycenter in L q ( X , m ) , with q dual exponent of p ∈ ( 1 , ∞ ) . We apply this general duality principle to study null sets for families of parametric and non-parametric curves in X . In the final part of the paper we provide a new proof, independent of optimal transportation, of the equivalence...

On the infinite time horizon linear-quadratic regulator problem under a fractional brownian perturbation

Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2005)

ESAIM: Probability and Statistics

In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic gaussian regulator problem. For a completely observable controlled linear system driven by a fractional brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.

On the infinite time horizon linear-quadratic regulator problem under a fractional Brownian perturbation

Marina L. Kleptsyna, Alain Le Breton, Michel Viot (2010)

ESAIM: Probability and Statistics

In this paper we solve the basic fractional analogue of the classical infinite time horizon linear-quadratic Gaussian regulator problem. For a completely observable controlled linear system driven by a fractional Brownian motion, we describe explicitely the optimal control policy which minimizes an asymptotic quadratic performance criterion.

On the inverse problem of the calculus of variations for ordinary differential equations

Olga Krupková (1993)

Mathematica Bohemica

Lepagean 2-form as a globally defined, closed counterpart of higher-order variational equations on fibered manifolds over one-dimensional bases is introduced, and elementary proofs of the basic theorems concerning the inverse problem of the calculus of variations, based on the notion of Lepagean 2-form and its properties, are given.

On the inverse variational problem in nonholonomic mechanics

Olga Rossi, Jana Musilová (2012)

Communications in Mathematics

The inverse problem of the calculus of variations in a nonholonomic setting is studied. The concept of constraint variationality is introduced on the basis of a recently discovered nonholonomic variational principle. Variational properties of first order mechanical systems with general nonholonomic constraints are studied. It is shown that constraint variationality is equivalent with the existence of a closed representative in the class of 2-forms determining the nonholonomic system. Together with...

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