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An algorithm for construction of ε-value functions for the Bolza control problem

Edyta Jacewicz (2001)

International Journal of Applied Mathematics and Computer Science

The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper...

An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in Lp-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov...

An application of the Fourier transform to optimization of continuous 2-D systems

Vitali Dymkou, Michael Dymkov (2003)

International Journal of Applied Mathematics and Computer Science

This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.

An approximation theorem for sequences of linear strains and its applications

Kewei Zhang (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L 1 by the sequence of linear strains of mapping bounded in Sobolev space W 1 , p . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.

An approximation theorem for sequences of linear strains and its applications

Kewei Zhang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We establish an approximation theorem for a sequence of linear elastic strains approaching a compact set in L1 by the sequence of linear strains of mapping bounded in Sobolev space W1,p . We apply this result to establish equalities for semiconvex envelopes for functions defined on linear strains via a construction of quasiconvex functions with linear growth.

An autonomous vehicle sequencing problem at intersections: A genetic algorithm approach

Fei Yan, Mahjoub Dridi, Abdellah El Moudni (2013)

International Journal of Applied Mathematics and Computer Science

This paper addresses a vehicle sequencing problem for adjacent intersections under the framework of Autonomous Intersection Management (AIM). In the context of AIM, autonomous vehicles are considered to be independent individuals and the traffic control aims at deciding on an efficient vehicle passing sequence. Since there are considerable vehicle passing combinations, how to find an efficient vehicle passing sequence in a short time becomes a big challenge, especially for more than one intersection....

An elementary proof of Marcellini Sbordone semicontinuity theorem

Tomáš G. Roskovec, Filip Soudský (2023)

Kybernetika

The weak lower semicontinuity of the functional F ( u ) = ∫ Ω f ( x , u , ∇ u ) d x is a classical topic that was studied thoroughly. It was shown that if the function f is continuous and convex in the last variable, the functional is sequentially weakly lower semicontinuous on W 1 , p ( Ω ) . However, the known proofs use advanced instruments of real and functional analysis. Our aim here is to present a proof understandable even for students familiar only with the elementary measure theory.

An Elliptic Neumann Problem with Subcritical Nonlinearity

Jan Chabrowski, Kyril Tintarev (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

We establish the existence of a solution to the Neumann problem in the half-space with a subcritical nonlinearity on the boundary. Solutions are obtained through the constrained minimization or minimax. The existence of solutions depends on the shape of a boundary coefficient.

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