A Parallel Frank-Wolfe/gradient Projection Method for Optimal Control PDF Download
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Author: Gerard G. L. Meyer
Publisher:
ISBN:
Category : Parallel processing (Electronic computers)
Languages : en
Pages : 30
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Abstract: "We propose a new parametrized gradient projection algorithm for solving constrained large scale optimization problems, and in particular, discrete optimal control problems with linear constraints. We show that an adaptive choice of parameters results in considerable decrease in number of iterations required to reach a predetermined solution neighborhood, and that the algorithm can be implemented in parallel resulting in a further decrease in computational time. We demonstrate the efficiency of the approach by comparing implementations on both the Cray 2 and Connection Machine 2. Numerical results are provided in solving discrete optimal control problems with very high dimensionality (up to 2,000,000 variables)."
Author: Gerard G. L. Meyer
Publisher:
ISBN:
Category : Parallel processing (Electronic computers)
Languages : en
Pages : 30
Get Book Here
Book Description
Abstract: "We propose a new parametrized gradient projection algorithm for solving constrained large scale optimization problems, and in particular, discrete optimal control problems with linear constraints. We show that an adaptive choice of parameters results in considerable decrease in number of iterations required to reach a predetermined solution neighborhood, and that the algorithm can be implemented in parallel resulting in a further decrease in computational time. We demonstrate the efficiency of the approach by comparing implementations on both the Cray 2 and Connection Machine 2. Numerical results are provided in solving discrete optimal control problems with very high dimensionality (up to 2,000,000 variables)."
Author: James R. Conley
Publisher:
ISBN:
Category :
Languages : en
Pages : 116
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Author: G. G. L. Meyer
Publisher:
ISBN:
Category :
Languages : en
Pages : 75
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Author:
Publisher:
ISBN:
Category : Smart materials
Languages : en
Pages : 520
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Author: Tiehong Tian
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ISBN:
Category :
Languages : en
Pages : 146
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Author:
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ISBN:
Category : Aeronautics
Languages : en
Pages : 1146
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Author:
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ISBN:
Category :
Languages : en
Pages : 7
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Author: John Kendall Willoughby
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ISBN:
Category : Adaptive control systems
Languages : en
Pages : 128
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The method of conjugate gradients (CG) has been shown to be a rapidly converging and efficient means of solving unconstrained optimal control problems. This dissertation presents some theoretical and computational characteristics of three modifications to the CG algorithm which make it applicable to control problems with terminal state variable constraints. The penalty function method and the projection method have been used to adapt ordinary gradient methods to constrained problems. It is concluded here that the penalty function technique is no more or less advantageous with the CG method than with other gradient techniques. The projection method is shown to be theoretically less compatible with the CG algorithm than with other gradient methods. However, a stepsize adjustment policy is suggested that preserves the rapid convergence that is characteristic of the CG method. It is also shown that nonlinear instead of linear terminal constraints cause no additional theoretical of computational difficulty. A third adaptation of the CG method is given which is original to this study. The method, called the modified conjugate gradient method (MCG), is applied to constrained problems by using constant Lagrange multipliers which converge to their optimal values as the iteration proceeds. A unique feature of the MCG method is that each control iterate produced by the method causes the constraints to be satisfied exactly. Furthermore, the technique is equally applicable to nonlinear and linear terminal state constraints. (Author).
Author: B.A.M. Piggott
Publisher:
ISBN:
Category :
Languages : en
Pages : 26
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Author: Henry Ekah-Kunde
Publisher:
ISBN: 9783668494169
Category :
Languages : en
Pages : 30
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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.
