Author: Henry Ekah-Kunde
Publisher: GRIN Verlag
ISBN: 3668494150
Category : Mathematics
Languages : en
Pages : 29
Book Description
Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In this research, a novel method to approximate the solution of optimal control problems governed by Volterra integral equations of weakly singular types is proposed. The method introduced here is the conjugate gradient method with a discretization of the problem based on the collocation approach on graded mesh points for non linear Volterra integral equations with singular kernels. Necessary and sufficient optimality conditions for optimal control problems are also discussed. Some examples are presented to demonstrate the efficiency of the method.
Conjugate gradient method for the solution of optimal control problems governed by weakly singular Volterra integral equations with the use of the collocation method
Author: Henry Ekah-Kunde
Publisher: GRIN Verlag
ISBN: 3668494150
Category : Mathematics
Languages : en
Pages : 29
Book Description
Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In this research, a novel method to approximate the solution of optimal control problems governed by Volterra integral equations of weakly singular types is proposed. The method introduced here is the conjugate gradient method with a discretization of the problem based on the collocation approach on graded mesh points for non linear Volterra integral equations with singular kernels. Necessary and sufficient optimality conditions for optimal control problems are also discussed. Some examples are presented to demonstrate the efficiency of the method.
Publisher: GRIN Verlag
ISBN: 3668494150
Category : Mathematics
Languages : en
Pages : 29
Book Description
Seminar paper from the year 2015 in the subject Mathematics - Applied Mathematics, grade: A, , language: English, abstract: In this research, a novel method to approximate the solution of optimal control problems governed by Volterra integral equations of weakly singular types is proposed. The method introduced here is the conjugate gradient method with a discretization of the problem based on the collocation approach on graded mesh points for non linear Volterra integral equations with singular kernels. Necessary and sufficient optimality conditions for optimal control problems are also discussed. Some examples are presented to demonstrate the efficiency of the method.
The Conjugate Gradient Method for Optimal Control Problems
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 7
Book Description
Applied Mechanics Reviews
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 784
Book Description
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 784
Book Description
Conjugate Gradient Type Methods for Ill-Posed Problems
Author: Martin Hanke
Publisher: CRC Press
ISBN: 1351458337
Category : Mathematics
Languages : en
Pages : 144
Book Description
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
Publisher: CRC Press
ISBN: 1351458337
Category : Mathematics
Languages : en
Pages : 144
Book Description
The conjugate gradient method is a powerful tool for the iterative solution of self-adjoint operator equations in Hilbert space.This volume summarizes and extends the developments of the past decade concerning the applicability of the conjugate gradient method (and some of its variants) to ill posed problems and their regularization. Such problems occur in applications from almost all natural and technical sciences, including astronomical and geophysical imaging, signal analysis, computerized tomography, inverse heat transfer problems, and many more This Research Note presents a unifying analysis of an entire family of conjugate gradient type methods. Most of the results are as yet unpublished, or obscured in the Russian literature. Beginning with the original results by Nemirovskii and others for minimal residual type methods, equally sharp convergence results are then derived with a different technique for the classical Hestenes-Stiefel algorithm. In the final chapter some of these results are extended to selfadjoint indefinite operator equations. The main tool for the analysis is the connection of conjugate gradient type methods to real orthogonal polynomials, and elementary properties of these polynomials. These prerequisites are provided in a first chapter. Applications to image reconstruction and inverse heat transfer problems are pointed out, and exemplarily numerical results are shown for these applications.
Conjugate Gradient Approach for Discrete Time Optimal Control Problems with Model-Reality Differences
Author: Sie Long Kek
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 0
Book Description
In this chapter, an efficient computation approach is proposed for solving a general class of discrete-time optimal control problems. In our approach, a simplified optimal control model, which is adding the adjusted parameters into the model used, is solved iteratively. In this way, the differences between the real plant and the model used are calculated, in turn, to update the optimal solution of the model used. During the computation procedure, the equivalent optimization problem is formulated, where the conjugate gradient algorithm is applied in solving the optimization problem. On this basis, the optimal solution of the modified model-based optimal control problem is obtained repeatedly. Once the convergence is achieved, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, both linear and nonlinear examples are demonstrated to show the performance of the approach proposed. In conclusion, the efficiency of the approach proposed is highly presented.
Publisher:
ISBN:
Category : Electronic books
Languages : en
Pages : 0
Book Description
In this chapter, an efficient computation approach is proposed for solving a general class of discrete-time optimal control problems. In our approach, a simplified optimal control model, which is adding the adjusted parameters into the model used, is solved iteratively. In this way, the differences between the real plant and the model used are calculated, in turn, to update the optimal solution of the model used. During the computation procedure, the equivalent optimization problem is formulated, where the conjugate gradient algorithm is applied in solving the optimization problem. On this basis, the optimal solution of the modified model-based optimal control problem is obtained repeatedly. Once the convergence is achieved, the iterative solution approximates to the correct optimal solution of the original optimal control problem, in spite of model-reality differences. For illustration, both linear and nonlinear examples are demonstrated to show the performance of the approach proposed. In conclusion, the efficiency of the approach proposed is highly presented.
Government reports annual index
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 1362
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 1362
Book Description
Some Applications of Gradient Methods
Author: Joseph W. Fischbach
Publisher:
ISBN:
Category : Conjugate gradient methods
Languages : en
Pages : 30
Book Description
Publisher:
ISBN:
Category : Conjugate gradient methods
Languages : en
Pages : 30
Book Description
A Combined Newton-Raphson and Gradient Parameter Correction Technique for Solution of Optimal-control Problems
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 76
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 76
Book Description
Method of Conjugate Gradients for Optimal Control Problems with State Variable Constraint
Author: Thomas Shu Fong
Publisher:
ISBN:
Category : Mathematical optimization
Languages : en
Pages : 176
Book Description
Publisher:
ISBN:
Category : Mathematical optimization
Languages : en
Pages : 176
Book Description
Method of Conjugate Gradients for Optimal Control Problems with State Variable Constraints
Author: T. S. Fong
Publisher:
ISBN:
Category :
Languages : en
Pages : 94
Book Description
A review of the computational method of conjugate gradients for linear and nonlinear operator equations is given with emphasis in applying this technique to state variable constraint control problems. The first and second Frechet derivatives of the performance functional are derived. The search directions generated in the iteration process for the optimal control are locally conjugate with respect to the second Frechet derivative. The convergence is along the expanding sequence of sets, the itersection of the linear spaces spanned by the search directions and the set of admissible controls. The computational technique is applied to two state variable constraint problems, in one of which a penalty function is employed to convert the constraint problem to an unconstrained one in addition to the approach considering the constraints directly. For this same problem the method of steepest descent also is studied, and comparison of the results obtained is made and discussed. (author).
Publisher:
ISBN:
Category :
Languages : en
Pages : 94
Book Description
A review of the computational method of conjugate gradients for linear and nonlinear operator equations is given with emphasis in applying this technique to state variable constraint control problems. The first and second Frechet derivatives of the performance functional are derived. The search directions generated in the iteration process for the optimal control are locally conjugate with respect to the second Frechet derivative. The convergence is along the expanding sequence of sets, the itersection of the linear spaces spanned by the search directions and the set of admissible controls. The computational technique is applied to two state variable constraint problems, in one of which a penalty function is employed to convert the constraint problem to an unconstrained one in addition to the approach considering the constraints directly. For this same problem the method of steepest descent also is studied, and comparison of the results obtained is made and discussed. (author).