Displaying similar documents to “Approximation of the pareto optimal set for multiobjective optimal control problems using viability kernels”

A problem of optimal control with free initial state

Mohamed Aidene, Kahina Louadj (2012)

ESAIM: Proceedings

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We are studying an optimal control problem with free initial condition. The initial state of the optimized system is not known exactly, information on initial state is exhausted by inclusions  ∈  . Accessible controls for optimization of continuous dynamic system are discrete controls defined on quantized axes. The method presented is based on the concepts and operations of the adaptive method [9] of linear programming. The results are illustrated by a...

Mean-Field Optimal Control

Massimo Fornasier, Francesco Solombrino (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We introduce the concept of 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 with each other, by simplifying...

Global optimality conditions for a dynamic blocking problem

Alberto Bressan, Tao Wang (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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The paper is concerned with a class of optimal blocking problems in the plane. We consider a time dependent set () ⊂ ℝ, described as the reachable set for a differential inclusion. To restrict its growth, a barrier can be constructed, in real time. This is a one-dimensional rectifiable set which blocks the trajectories of the differential inclusion. In this paper we introduce a definition of “regular strategy”, based on a careful classification of blocking arcs. Moreover, we derive...

Global optimality conditions for a dynamic blocking problem

Alberto Bressan, Tao Wang (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

The paper is concerned with a class of optimal blocking problems in the plane. We consider a time dependent set () ⊂ ℝ, described as the reachable set for a differential inclusion. To restrict its growth, a barrier can be constructed, in real time. This is a one-dimensional rectifiable set which blocks the trajectories of the differential inclusion. In this paper we introduce a definition of “regular strategy”, based on a careful classification...

Parallel approximation to high multiplicity scheduling problems smooth multi-valued quadratic programming

Maria Serna, Fatos Xhafa (2007)

RAIRO - Theoretical Informatics and Applications

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We consider the parallel approximability of two problems arising from high multiplicity scheduling, namely the and the . These two problems are known to be modelled by a class of quadratic programs that are efficiently solvable in polynomial time. On the parallel setting, both problems are -complete and hence cannot be efficiently solved in parallel unless  = . To deal with the parallel approximablity of these problems, we show first a parallel approximation procedure to a subclass...

New regularity results and improved error estimates for optimal control problems with state constraints

Eduardo Casas, Mariano Mateos, Boris Vexler (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we are concerned with a distributed optimal control problem governed by an elliptic partial differential equation. State constraints of box type are considered. We show that the Lagrange multiplier associated with the state constraints, which is known to be a measure, is indeed more regular under quite general assumptions. We discretize the problem by continuous piecewise linear finite elements and we are able to prove that, for the case of a linear equation, the order...

Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs

Abdellah Chkifa, Albert Cohen, Ronald DeVore, Christoph Schwab (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The numerical approximation of parametric partial differential equations is a computational challenge, in particular when the number of involved parameter is large. This paper considers a model class of second order, linear, parametric, elliptic PDEs on a bounded domain with diffusion coefficients depending on the parameters in an affine manner. For such models, it was shown in [9, 10] that under very weak assumptions on the diffusion coefficients, the entire family of solutions to...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...

Two dimensional optimal transportation problem for a distance cost with a convex constraint

Ping Chen, Feida Jiang, Xiaoping Yang (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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We first prove existence and uniqueness of optimal transportation maps for the Monge’s problem associated to a cost function with a strictly convex constraint in the Euclidean plane ℝ. The cost function coincides with the Euclidean distance if the displacement  −  belongs to a given strictly convex set, and it is infinite otherwise. Secondly, we give a sufficient condition for existence and uniqueness of optimal transportation maps for the original Monge’s problem in ℝ. Finally, we get...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. ...

Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1

Tiziana Durante, Taras A. Mel’nyk (2012)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider quasilinear optimal control problems involving a thick two-level junction which consists of the junction body and a large number of thin cylinders with the cross-section of order 𝒪( ). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. ...