27,993 research outputs found
On attainability of optimal controls in coefficients for system of Hammerstein type with anisotropic p-Laplacian
No full textIn this paper we consider an optimal control
problem (OCP) for the coupled system of a nonlinear monotone Dirichlet problem with anisotropic p-Laplacian and matrix-valued L^infinity(Omega, R^(NxN))-controls in its coefficients
and a nonlinear equation of Hammerstein type. Using the direct
method in calculus of variations, we prove the existence of an optimal control in considered problem and provide sensitivity analysis for a specific case of considered problem with respect to two-parameter regularization
On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality
Get PDFWe consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions
Shape stability of optimal control problems in coefficients for coupled system of Hammerstein type
No full textIn this paper we consider an optimal control problem (OCP) for
the coupled system of a nonlinear monotone Dirichlet problem with matrixvalued
L^Infinity(Ω;R^NxN)-controls in coefficients and a nonlinear equation of Hammerstein
type. Since problems of this type have no solutions in general, we
make a special assumption on the coefficients of the state equation and introduce
the class of so-called solenoidal admissible controls. Using the direct
method in calculus of variations, we prove the existence of an optimal control.
We also study the stability of the optimal control problem with respect to the
domain perturbation. In particular, we derive the sufficient conditions of the
Mosco-stability for the given class of OCPs
On optimality conditions for optimal control problem in coefficients for Delta_p-Laplacian
Get PDFIn this paper we study an optimal control problem for a nonlinear monotone Dirichlet problem where the control is taken as L^infinity(Omega) coefficient of Delta_p-Laplacian. Given a cost function, the objective is to derive first-order optimality conditions and provide their substantiation. We propose some ideas and new results concerning the differentiability properties of the Lagrange functional associated with the considered control problem. The obtained adjoint boundary value problem is not coercive and, hence, it may admit infinitely many solutions. That is why we concentrate not only on deriving the adjoint system, but also, following the well-known Hardy-Poincaré Inequality, on a formulation of sufficient conditions which would guarantee the uniqueness of the adjoint state to the optimal pair
On Boundary Optimal Control Problem for an Arterial System: First-Order Optimality Conditions
No full textWe discuss a control constrained boundary optimal control problem for the Boussinesq-type system arising in the study of the dynamics of an arterial network. We suppose that the control object is described by an initial-boundary value problem for 1D system of pseudo-parabolic nonlinear equations with an unbounded coecient in the principle part and the Robintype of boundary conditions. The main question we study in this part of the paper is about the existence of optimal solutions and rst-order optimality conditions
On a Variational Problem with Nonstandard Growth Functional and its Applications to Image Processing
No full textWe propose a new variational model in Sobolev-Orlicz spaces with non-standard growth conditions of the objective functional and discuss its applications to image processing. The characteristic feature of the proposed model is that the variable exponent, which is associated with non-standard growth, is unknown a priori and it depends on a particular function that belongs to the domain of objective functional. So, we deal with a constrained minimization problem that lives in variable Sobolev-Orlicz spaces. In view of this, we discuss the consistency of the proposed model, give the scheme for its regularization, derive the corresponding optimality system, and propose an iterative algorithm for practical implementations
On Variational Model in Sobolev-Orlicz Spaces for Spatiotemporal Interpolation of Multi-Spectral Satellite Images
No full textWe propose a new two-level variational model in Sobolev-Orlicz spaces with non-standard growth conditions of the objective functional and discuss its applications to the spatiotemporal interpolation of multi-spectral satellite images. At
the first level, we deal with the temporal interpolation problem that can be cast as a state constrained optimal control problem for anisotropic convection-diffusion equation, whereas at the second level we solve a constrained minimization problem with a nonstandard growth energy functional that lives in variable Sobolev-Orlicz spaces. The characteristic feature of the proposed model is the fact that the variable exponent, which is associated with non-standard growth in spatial interpolation problem, is unknown a priori and it depends on the solution of the firstlevel optimal control problem. It makes this spatiotemporal interpolation problem rather challenging. In view of this, we discuss the consistency of the proposed model, study the existence of optimal solutions, and derive the corresponding optimality systems. In particular, we apply this approach to the well-known prediction problem of the Daily MODIS Surface Reflectance at the Landsat-Like Resolution
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On Henig Regularization of State-Constrained Optimal Control Problem for the p-Laplace Equation
Get PDFWe study a Dirichlet optimal control problem for a quasilinear monotone p-Laplace equation with control and state constraints. The coefficient of the p-Laplacian, the weight u, we take as a control in L1(Ω). We discuss a relaxation of such problem following the so-called Henig regularization scheme.</span
Гьольдерова непрерывность зависимости коэффициентов от резольвенты краевой задачи Дирихле с анизотропным p-лапласианом
No full textВ работе исследуется свойство гьольдеровой непрерывности обратного отображения, определяющего матрицу коэффициентов диффузии A(x) в главной части квази-линейного эллиптического уравнения с анизотропным p-лапласианом как функцию оператора резольвенты. Доказано, что на выбранном классе допустимых матриц с негладкими коэффициентами резольвента однозначно определяет матрицу коэффициентов диффузии и данное обратное отображение является непрерывным по Гьольдеру в соответствующих топологиях
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