共查询到20条相似文献,搜索用时 31 毫秒
1.
《Nonlinear Analysis: Theory, Methods & Applications》2011,74(10):3242-3260
The purpose of this paper is to propose and study a mathematical model and a boundary control problem associated to the miscible displacement of hydrogen through the porous anode of a PEM fuel cell. Throughout the paper, we study certain variational problems with a priori regularity properties of the weak solutions. We obtain the existence of less regular solutions and then we prove the desired regularity of these solutions. We consider a control problem that permits to determine the boundary distribution of the pressure which provides an optimal configuration for the temperature and for the concentration, as well. Since the solution of the problem is not unique, the control variable does not appear explicitly in the definition of our cost functional. To overcome this difficulty, we introduce a family of penalized control problems which approximates our boundary control problem. The necessary conditions of optimality are derived by passing to the limit in the penalized optimality conditions. 相似文献
2.
We consider a nonlinear antiplane problem which models the deformation of an elastic cylindrical body in frictional contact with a rigid foundation. The contact is modelled with Tresca’s law of dry friction in which the friction bound is slip dependent.The aim of this article is to study an optimal control problem which consists of leading the stress tensor as close as possible to a given target, by acting with a control on the boundary of the body. The existence of at least one optimal control is proved. Next we introduce a regularized problem, depending on a small parameter ρ, and we study the convergence of the optimal controls when ρ tends to zero. An optimality condition is delivered for the regularized problem. 相似文献
3.
We consider the fast and efficient numerical solution of linear-quadratic optimal control problems with additional constraints on the control. Discretization of the first-order conditions leads to an indefinite linear system of saddle point type with additional complementarity conditions due to the control constraints. The complementarity conditions are treated by a primal-dual active set strategy that serves as outer iteration. At each iteration step, a KKT system has to be solved. Here, we develop a multigrid method for its fast solution. To this end, we use a smoother which is based on an inexact constraint preconditioner.We present numerical results which show that the proposed multigrid method possesses convergence rates of the same order as for the underlying (elliptic) PDE problem. Furthermore, when combined with a nested iteration, the solver is of optimal complexity and achieves the solution of the optimization problem at only a small multiple of the cost for the PDE solution. 相似文献
4.
Grossman C. 《Numerical Functional Analysis & Optimization》2013,34(1-2):159-173
By means of an additional substitution a parabolic control problem with some nonlinear boundary condition will be decoupled into some control problem with linear parabolic state equations and an appropriate nonlinear mapping. This separation allows the use of efficient techniques e.g. Fourier methods, to determine the solution of linear parabolic state equations. Essential properties of the mapping used in the transformation are studied. Further, the application of piecewise constant discretizations of the controls in connection with the proposed splitting is discussed. 相似文献
5.
We consider the optimization problem of minimizing with a constraint on the volume of {u>0}. We consider a penalization problem, and we prove that for small values of the penalization parameter, the constrained volume is attained. In this way we prove that every solution u is locally Lipschitz continuous and that the free boundary, ∂{u>0}∩Ω, is smooth. 相似文献
6.
Friedemann Schuricht 《Archiv der Mathematik》2006,87(6):572-577
Minimizers of the total variation subject to a prescribed
-norm are considered as eigensolutions of the 1-Laplace operator. The derivation of the corresponding eigenvalue equation,
which requires particular care due to the lack of smoothness, is carried out in a previous paper by using particular methods
of nonsmooth analysis. The present paper provides a simpler proof that exploits the special structure of the problem.
Received: 8 December 2005 相似文献
7.
L.J. Alvarez-Vázquez A. Martínez M.E. Vázquez-Méndez M.A. Vilar 《Journal of Computational and Applied Mathematics》2008
Fishways are the main type of hydraulic devices currently used to facilitate migration of fish past obstructions (dams, waterfalls, rapids,…) in rivers. In this paper we present a mathematical formulation of an optimal control problem related to the optimal management of a vertical slot fishway, where the state system is given by the shallow water equations, the control is the flux of inflow water, and the cost function reflects the need of rest areas for fish and of a water velocity suitable for fish leaping and swimming capabilities. We give a first-order optimality condition for characterizing the optimal solutions of this problem. From a numerical point of view, we use a characteristic-Galerkin method for solving the shallow water equations, and we use an optimization algorithm for the computation of the optimal control. Finally, we present numerical results obtained for the realistic case of a standard nine pools fishway. 相似文献
8.
L.J. Alvarez-Vázquez A. Martínez 《Journal of Computational and Applied Mathematics》2010,234(4):1267-1276
This work is devoted to the numerical resolution of an optimal control problem that arises in the management of a reservoir for the remediation of a polluted river section. By using mathematical modeling and optimal control techniques we set the mathematical formulation of the problem (as a hyperbolic optimal control problem with control constraints), and obtain a fully discretized problem. Finally, we propose a gradient-free method to solve it, and present realistic numerical results. 相似文献
9.
Summary.
An optimal control problem
for impressed cathodic systems in electrochemistry is studied.
The control in this problem is the current
density on the anode. A matching objective functional is
considered. We first demonstrate the existence and uniqueness
of solutions for the governing partial differential equation
with a nonlinear boundary condition. We then prove
the existence of an optimal solution.
Next, we derive a necessary condition of optimality
and establish an optimality system of equations.
Finally, we define a finite element algorithm and
derive optimal error estimates.
Received
March 10, 1993 / Revised version received July 4, 1994 相似文献
10.
Carlo Mariconda 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(4):828-801
Let w∗(x)=a⋅x+b be an affine function in RN, Ω⊂RN, L:RN→R be convex and w be a local minimizer of
11.
Optimal control for a system consistent of the viscosity dependent Stokes equations coupled with a transport equation for the viscosity is studied. Motivated by a lack of sufficient regularity of the adjoint equations, artificial diffusion is introduced to the transport equation. The asymptotic behavior of the regularized system is investigated. Optimality conditions for the regularized optimal control problems are obtained and again the asymptotic behavior is analyzed. The lack of uniqueness of solutions to the underlying system is another source of difficulties for the problem under investigation. 相似文献
12.
We consider an elliptic optimal control problem with control constraints and pointwise bounds on the gradient of the state.
We present a tailored finite element approximation to this optimal control problem, where the cost functional is approximated
by a sequence of functionals which are obtained by discretizing the state equation with the help of the lowest order Raviart–Thomas
mixed finite element. Pointwise bounds on the gradient variable are enforced in the elements of the triangulation. Controls
are not discretized. Error bounds for control and state are obtained in two and three space dimensions. A numerical example
confirms our analytical findings. 相似文献
13.
An optimal design problem with perimeter penalization 总被引:11,自引:0,他引:11
Luigi Ambrosio Giuseppe Buttazzo 《Calculus of Variations and Partial Differential Equations》1993,1(1):55-69
We study the optimal design problem of finding the minimal energy configuration for a mixture of two conducting materials when a perimeter penalization of the unknown domain is added. We show that in this situation an optimal domain exists and that, under suitable assumptions on the data, it is an open set.This work is part of the project EURHomogenization, contract SC1-CT91-0732 of the program SCIENCE of the Commission of the European Communities. 相似文献
14.
We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich
equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical
approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both
cases some examples are presented.
Received February 10, 2000 / final version received July 21, 2000?Published online November 8, 2000 相似文献
15.
A. D. Ioffe R. T. Rockafellar 《Calculus of Variations and Partial Differential Equations》1996,4(1):59-87
Necessary conditions are developed for a general problem in the calculus of variations in which the Lagrangian function, although finite, need not be Lipschitz continuous or convex in the velocity argument. For the first time in such a broadly nonsmooth, nonconvex setting, a full subgradient version of Euler's equation is derived for an arc that furnishes a local minimum in the classical weak sense, and the Weierstrass inequality is shown to accompany it when the arc gives a local minimum in the strong sense. The results are achieved through new techniques in nonsmooth analysis.This research was supported in part by funds from the U.S.-Israel Science Foundation under grant 90-00455, and also by the Fund for the Promotion of Research at the Technion under grant 100-954 and by the U.S. National Science Foundation under grant DMS-9200303.This article was processed by the author using the
style filepljourlm from Springer-Verlag. 相似文献
16.
In this paper, we consider a free boundary problem with volume constraint. We show that positive minimizer is locally Lipschitz
and the free boundary is analytic away from a singular set with Hausdorff dimension at most n − 8. 相似文献
17.
J. Frédéric Bonnans Audrey Hermant 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009
This paper deals with the optimal control problem of an ordinary differential equation with several pure state constraints, of arbitrary orders, as well as mixed control-state constraints. We assume (i) the control to be continuous and the strengthened Legendre–Clebsch condition to hold, and (ii) a linear independence condition of the active constraints at their respective order to hold. We give a complete analysis of the smoothness and junction conditions of the control and of the constraints multipliers. This allows us to obtain, when there are finitely many nontangential junction points, a theory of no-gap second-order optimality conditions and a characterization of the well-posedness of the shooting algorithm. These results generalize those obtained in the case of a scalar-valued state constraint and a scalar-valued control. 相似文献
18.
19.
D. Russell Luke 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(3):1531-1546
The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von Neumann has been shown to converge locally at a linear rate dependent on the regularity modulus of the intersection. In many applications, however, the sets in question come from inexact measurements that are matched to idealized models. It is unlikely that any such problems in applications will enjoy metrically regular intersection, let alone set intersection. We explore a regularization strategy that generates an intersection with the desired regularity properties. The regularization, however, can lead to a significant increase in computational complexity. In a further refinement, we investigate and prove linear convergence of an approximate alternating projection algorithm. The analysis provides a regularization strategy that fits naturally with many ill-posed inverse problems, and a mathematically sound stopping criterion for extrapolated, approximate algorithms. The theory is demonstrated on the phase retrieval problem with experimental data. The conventional early termination applied in practice to unregularized, consistent problems in diffraction imaging can be justified fully in the framework of this analysis providing, for the first time, proof of convergence of alternating approximate projections for finite dimensional, consistent phase retrieval problems. 相似文献
20.
We study a variational approach, called Generalized Minimizing Movemenents (GMM) and proposed by E. De Giorgi, to evolution
of hypersurfaces by mean curvature in the case of a Dirichlet boundary datum. We prove an existence theorem of a GMM when
on the initial solid are made suitable geometric hypotheses.
Sunto Si studia un approccio variazionale, detto Movimenti Minimizzanti Generalizzati (GMM) e proposto da Ennio De Giorgi, per l’evoluzione di una ipersuperficie secondo la curvatura media con un dato al bordo di tipo Dirichlet. Viene provato un teorema di esistenza quando sul solido iniziale siano fatte opportune ipotesi di tipo geometrico.相似文献