Francis Benyah | University Of Cape Coast, Ghana (original) (raw)

Papers by Francis Benyah

Journal of mathematics and statistics, 2024

Springer eBooks, 2001

This article presents a summary of work undertaken to quantify aspects of the ill-conditioning en... more This article presents a summary of work undertaken to quantify aspects of the ill-conditioning encountered in the computations of optimal control problems. A mathematical machinery for the quantification of aspects of ill-conditioning is developed. This is then used to study how ill-conditioning varies with the size of discretization of control functions, and how it varies with different basis functions. The ill-conditioning associated with two different computational algorithms are also compared. A regularization method is used to obtain a stable and smooth solution. Implementation in the optimal control software MISER3 and computation of test examples involving various constraint types are considered.

Nonlinear Analysis-theory Methods & Applications, Aug 1, 2001

International Journal of Analysis and Applications, Mar 5, 2021

The paper considers the problem of least squares minimization with L 1-norm regularization functi... more The paper considers the problem of least squares minimization with L 1-norm regularization functional. It investigates various smoothing approximations for the L 1-norm functional. It considers Quadratic, Sigmoid and Cubic Hermite functionals. A Tikhonov regularization is then applied to each of the resulting smooth least squares minimization problem. Results of numerical simulations for each smoothing approximation are presented. The results indicate that our regularization method is as good as any other non-smoothing method used in developed solvers.

Australian & New Zealand industrial and applied mathematics journal, Jun 14, 2002

The Control Parametrization Enhancing Technique (cpet), is extended to a general class of constra... more The Control Parametrization Enhancing Technique (cpet), is extended to a general class of constrained time-delayed optimal control problems. A model transformation approach is used to convert the time-delayed problem to an optimal control problem involving mixed boundary conditions, but without time-delayed arguments. The cpet is then used to solve this non delayed problem. Two test examples have been solved to illustrate the efficiencies of the cpet for time delayed problems.

International Journal of Analysis and Applications, 2021

Mathematical Modelling and Applications, 2020

In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow ... more In this paper, the problem of ill-posedness of solution in identifying multiple groundwater flow parameters from hydraulic head data and other ancillary data was assessed. The solution approach to the parameter identification problem is sought by applying the Least Squares, the Adjoint, the Conjugate Gradient Method and a proposed Parameter Transformation Method. Numerical test for a 1D and 2D flow models governed by PDEs were used to assess the accuracy and stability of the proposed method. The proposed method gave an appreciable solution estimates with minimal error-norm compared with the o ptimisation techniques explored in the study as a measure to the PTM The results revealed that when the adapted methods and the PTM were simulated numerically on a 1D and 2D test problems, the PTM gave a more stable solution estimates with a residual norm-error value of 2.23500 for the 1D test problem compared with that of the Adjoint method which prove to be the comparing solution with a norm-error value of 2.66500. For the 2D test case, the results also revealed that the PTM was stable with a residual norm-error value of 10.98310 compared with that of the Conjugate Gradient method with value of 86.562. Thus in conclusion, the study revealed that the PTM is capable of yielding realistic solution estimates compared with the studied optimisation methods.

Abstract.We consider an SIR model with variable size population and formulate an optimal control ... more Abstract.We consider an SIR model with variable size population and formulate an optimal control problem subject to the model with vaccination and treatment as controls. Our aim is to find the optimal combination of vaccination and treatment strategies that will minimize the cost of the two control measures as well as the number of infectives. Our model analyses show that the disease free equilibrium is globally asymptoti-cally stable if the basic reproduction number is less than unity while the endemic equilibrium exists and it is globally asymptotically stable whenever the basic reproduction number is greater than unity. We used Pon-tryagin’s maximum principle to characterize the optimal levels of the two controls. The resulting optimality system is solved numerically. The results show that the optimal combination of vaccination and treatment strategy required to achieve the set objective will depend on the relative cost of each of the control measures. The results from our simula...

Journal of Mathematics Research

This paper examined the problem of ill-posedness of solution in identifying parameters from a giv... more This paper examined the problem of ill-posedness of solution in identifying parameters from a given groundwater flow model. The solution approach to the problem was attempted by the method of Parameter Transformation coupled with Tikhonov Regularisation with and without Truncation which has not been explored. Convergence of the method was assessed by the L-Curve criterion. Numerical examples were presented to illustrate the efficiency of the proposed Regularisation Technique. Tikhonov Regularisation with Truncation turns to give a more realistic solution estimates when examined numerically, compared to that of Regularisation without Truncation.

Proceedings of the 10th Wseas International Conference on Telecommunications and Informatics and Microelectronics Nanoelectronics Optoelectronics and Wseas International Conference on Signal Processing, May 27, 2011

Optimal control computations are well known to be ill-conditioned, but there is little quantifiab... more Optimal control computations are well known to be ill-conditioned, but there is little quantifiable knowledge on the topic. The mathematical machinery for the quantification of ill-conditioning in optimal control computation is presented. Implementation in the optimal control software MISER3 and computation of test examples are discussed. Some idea of how the condition numbers vary with the number of discretization parameters for controls of typical problems is given. Various constraint types are considered and a comparison of two methods for computing smooth controls is presented.

Applied Optimization, 2001

Ill-conditioned linear systems arise in many applications, for example, in the solution of integr... more Ill-conditioned linear systems arise in many applications, for example, in the solution of integral equations, and in the solution of non-linear programming problems. In many application of linear algebra, the need arises to find a good approximation bx to a vector x 2 R,, by a nearby system that is less sensitive to the error in b and considers the computed,solution of the latter system an approximation of x. This replacement is known,as regularization. This essay examines various regularization methods,for computing,stable solution to ill-conditioned linear systems. i Contents

Nonlinear Analysis: Theory, Methods & Applications, 2001

Journal of Biological Dynamics, 2012

The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1999

Consider a general class of constrained optimal control problems in canonical form. Using the cla... more Consider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to conve...