Browsing by Author "Bamigbola, Olabode Matthias"
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Item Considering the depth of recursion in complexity measurement of algorithms(2012) Okeyinka, Aderemi E.; Bamigbola, Olabode MatthiasItem A Diagnostic Treatment of Unconstrained Optimization Problems via a Modified Armijo Line Search Technique(International Organization of Scientific Research, 2014) Bamigbola, Olabode Matthias; Adewumi, Aderemi O.; Adeleke, Olawale J.; Agarana, Michael C.The study of optimization is getting broader with every passing day. Optimization is basically the art of getting the best results under a given set of circumstances. A very simple but important class of optimization problems is the unconstrained problems. Several techniques have been developed to handle unconstrained problems, one of which is the conjugate gradient method (CGM), which is iterative in nature. In this work, we applied the nonlinear CGM to solve unconstrained problems using inexact line search techniques. We employed the well-known Armijo line search criterion and its modified form.Item Global Control Theory and Its Applications(Nova Science Publishers, 2015) Adewale, Timothy A.; Bamigbola, Olabode MatthiasThis chapter presents a controlled dynamic system whose state at any moment in time is described by the vector x. To control means that the systems equations are subdefinite. If this subdefiniteness with fixed t;x is represented by some non fixed element u, then controlling the system implies closing its equations by assigning the function u(t) or u(t;x). The assignment of u(t) is called the program of control. It is the aim of control to guide the system in the assigned conditions as reflected in the constraints imposed on the state x at the end of the control period t = t f , to provide process admissibility connected with fulfilment of current constraints imposed on the state x(t) fulfil some qualitative dynamic requirements set for the system, such as stability. In the process of solving these problems, some new mathematical ideas were suggested, namely , the theory of optimal control, developed as a synthesis of the classical variational calculus which makes use of Euler-Lagrange variation method. The first one is connected with generalization of conditions for a local minimum of the real variable function f (x) = 0; f (x) ≥ 0 to the problem of functional analysis. The second one is connected with imbedding the optimal process construction problem in the family of these problems for various initial conditions. The second method is more demanding and it culminates in global control theory. Methods of control improvement are discussed including computer methods or iterative techniques of control improvement, namely, the gradient method and needle method. The new idea of the theory of optimal control makes use of the approach based on sufficient conditions for global optimality of control processes and a mathematical technique for global estimates related to it. An interesting characteristic feature of the global estimates technique is the richness of the analytical medium created by this technique. Some areas of application are provided by the control of the pure inertia plant, sliding mass, sliding regimes, and electricity generation.Item Mathematical modeling of electric power flow and the minimization of power losses on transmission lines(Elsevier, 2014) Bamigbola, Olabode Matthias; Ali, Montaz; Oke, Michael O.The importance of electric power in today’s world cannot be overemphasized, for it is the key energy source for industrial, commercial and domestic activities. Its availability in the right quantity is essential to advancement of civilization. Electrical energy produced at power stations is transmitted to load centres from where it is distributed to the consumers through the use of transmission lines run from one place to another. As a result of the physical properties of the transmission medium, some of the transmitted power are lost to the surroundings. The power losses could take off a sizeable portion of the transmitted power since the transmission lines usually span a long distance, sometimes several hundred kilometers. The overall effect of power losses on the system is a reduction in the quantity of power available to the consumers. As such, adequate measures must be put in place to reduce power losses to the barest minimum. Thus, in this paper, we developed a mathematical model for determining power losses over typical transmission lines, as the resultant effect of ohmic and corona power losses, taking into cognizance the flow of current and voltage along the lines. Application of the classical optimization technique aided the formulation of an optimal strategy for minimization of power losses on transmission lines. With the aid of the new models it is possible to determine current and voltage along the transmission lines. In addition, we note that the analytical method does not involve any design or construction and so is less expensive than other models reported in the literature. Hence, the goal of this paper is to address a very well-known engineering problem – reducing the power losses on transmission lines to the barest minimum.Item A New Dogleg Method for Solving the Trust-Region Subproblem(International Organization of Scientific Research, 2013) Oruh, Ben I.; Bamigbola, Olabode MatthiasIn this paper a new dogleg method for solving the trust region subproblem where convergence is based on constructing two paths is presented. The condition on the paths is incorporated into an algorithm to determine the optimum point of a smooth function. Numerical experiments with some classical problems showed that the new dogleg method is robust and efficient.Item Numerical experiments on the conjugate gradient method with and without line search(International Institute of Academic Research and Development, 2016) Ajimoti, Adams; Bamigbola, Olabode MatthiasThe conjugate gradient method CGM is an effective iterative method which is widely used for solving large-scale unconstrained optimization problems due to its low memory requirement. The efficiency of the CGM depends majorly on the step-size. Line search technique has been used in various literatures to obtain the step-size. A very recent development is to obtain the step-size with a unified formula which is refereed to as step-size without line search. Hence, in this work, we present numerical experiments for well-known CGMs such as Fletcher-Reeves, Bamigbola-Ali-Nwaeze, Polak-Ribiere, Dai-Yuan, Liu-Storey, Hesten-Stiefel, Conjugate-Descent, Hager-Zhang and Gradient Search Conjugacy methods. Numerical results obtained are graphically illustrated using performance profiling software to compare numerical efficiency of five inexact line searches namely Armijo, Goldstein, Weak, Strong and Approximate Wolfe and two formulae for estimating the step-size without line search which are Wu formula and Ajimoti-Bamigbola formula.Item Numerical study of depth recursion in complexity measurement using Halstead measure(2012) Okeyinka, Aderemi E.; Bamigbola, Olabode MatthiasComplexity of algorithms has been studied analytically using the concept of Big O notation. One of the flaws of the study is that the complexities obtained for algorithms are in most cases the same; whereas in reality such algorithms might vary in terms of efficiency. The reason for the disparity is, of course, due to the definition of the Big O itself which mathematically is sound anyway. However, for pragmatic purposes, there is need for estimating actual complexities of each algorithm to be sure of which one is the best given more than one algorithms solving the same problem. In this study, recursion is considered and the complexities of recursive algorithms are estimated numerically using Halstead measure. Our findings show that recursive algorithms are more complex and hence less efficient than non-recursive algorithms.Item On Algebraic Structure of Improved Gauss-Seidel Iteration(World Academy of Science, Engineering and Technology, 2014) Bamigbola, Olabode Matthias; Ibrahim, Adebisi A.Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined apriori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss- Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss- Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.Item On controllability property of optimal control model of electric power generating system(Department of Science Education, Federal University of Technology, Minna, 2014) Aderinto, Yidiat O.; Bamigbola, Olabode MatthiasItem On optimum dispatch of electric power generation via numerical method(African Network of Scientific and Technical Institutions, 2013) Aderinto, Yidiat O.; Bamigbola, Olabode MatthiasIn this work we develop an optimum dispatch / generating strategy by presenting economically the best load flow configuration in supplying load demand among the generators. The main aim is to minimize the total production / generation costs, with minimum losses and at the same time satisfy the load flow equation without violating the inequality constraints.Item On the stability analysis of uncertain optimal control modelof management of net risky capital asset(International Institute of Academic Research and Development, 2016) Latunde, Tolulope; Bamigbola, Olabode MatthiasUncertain process is used in modeling uncertain occurrences that vary with time. The uncertain processes was used to study and model a special case of asset management problems. Thus, based on some conditions of stability, we herein give some stability theorems of the model.Item Optimal control applied to electric power generating systems model(Faculty of Physical Sciences, University of Ilorin, Ilorin, 2015) Aderinto, Yidiat O.; Bamigbola, Olabode MatthiasItem Optimal control of air pollution(Punjab University Press, 2017) Aderinto, Yidiat O.; Bamigbola, Olabode MatthiasIn this article, mathematical expressions that represent the dynamics of air pollution associated with electric power generating industries (in particular, atmospheric CO2) is proposed using an optimal control theory approach. The model is characterized via Pontryagin's maximum/minimum principles. Electric power plants efficiency improvement was introduced through applying technologies. The optimality system is established in attempt to minimize both the cost of applying technology for efficiency improvement as well as the atmospheric emission while maximizing the electric power generation output.Item Optimal hybrid BFGS-CG method for unconstrained optimization(Science Domain, 2018) Bamigbola, Olabode Matthias; Okundalaye, Oluwaseun O.; Ejieji, Catherine N.In solving unconstrained optimization problems, both quasi-Newton and conjugate gradient methods are known to be e cient methods. Hence, the optimal hybrid Broyden-Fletcher-Goldfarb-Shanno-Conjugate Gradient (OBFGS-CG) method is proposed in this work, which combines the strengths of both BFGS and CG methods. The optimal hybrid BFGS-CG method is based on an existing hybrid BFGS-CG method. The optimal BFGS-CG paramter, when utilised in solving unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time.Item Optimal hybrid BFGS-CG method for unconstrained optimization(Science Domain, 2018) Bamigbola, Olabode Matthias; Okundalaye, Oluwaseun O.; Ejieji, Catherine N.In solving unconstrained optimization problems, both quasi-Newton and conjugate gradient methods are known to be e cient methods. Hence, the optimal hybrid Broyden-Fletcher-Goldfarb-Shanno-Conjugate Gradient (OBFGS-CG) method is proposed in this work, which combines the strengths of both BFGS and CG methods. The optimal hybrid BFGS-CG method is based on an existing hybrid BFGS-CG method. The optimal BFGS-CG paramter, when utilised in solving unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time.Item Parameter estimation and sensitivity analysis of an optimal control model for capital asset management(Hindawi, 2018) Latunde, Tolulope; Bamigbola, Olabode MatthiasOptimal control is a very significant field ofmodern control theorywhich has been applied inmany areas like medicine, science, and finance.Thiswork is based on realization of asset values as a benefit of assetmanagementwhere a capital assetmanagement problem is modelled and expressedmathematically from the perspective of an investorwhose income is generated by return and capital gains on investments with price and return on assets assumed to satisfy uncertainty process. This results in an optimal control model based on uncertainty theory which relates two or more parameters that measures the condition or state of individual’s investments. These parameters enable us to know the condition of risk involved in asset management and how to maintain and manage the assets in order to maximize expected present value of the utility of asset and minimize the risk involved to aid capital investment decision-making. Parameter sensitivity analysis is an approach given to a model so as to define significance of the factors related to the model where the whole parameter space is fully described. However, the model is applied to a real-life problem of capital asset management to deal with debt crisis of a nation’s economy and the sensitivity analysis to determine the effects of the input factors on the model is investigated such that relative significance and sensitivity of each parameter on the model results are presented using parameter estimations. Finally the optimal control decision policy is obtained and discussed.Item Parameter estimation and sensitivity analysis of an optimalcontrol model for capital asset management(Hindawi, 2018) Latunde, Tolulope; Bamigbola, Olabode MatthiasOptimal control is a very significant field of modern control theory which has been applied inmany areas like medicine, science, and finance.This work is based on realization of asset values as a benefit of asset management where a capital asset management problem is modelled and expressed mathematically from the perspective of an investor whose income is generated by return and capital gains on investments with price and return on assets assumed to satisfy uncertainty process. This results in an optimal control model based on uncertainty theory which relates two or more parameters that measures the condition or state of individual’s investments. These parameters enable us to know the condition of risk involved in asset management and how to maintain and manage the assets in order to maximize expected present value of the utility of asset and minimize the risk involved to aid capital investment decision-making. Parameter sensitivity analysis is an approach given to a model so as to define significance of the factors related to the model where the whole parameter space is fully described. However, the model is applied to a real-life problem of capital asset management to deal with debt crisis of a nation’s economy and the sensitivity analysis to determine the effects of the input factors on the model is investigated such that relative significance and sensitivity of each parameter on the model results are presented using parameter estimations. Finally the optimal control decision policy is obtained and discussed.Item Predictive Models of Current, Voltage, and Power Losses on Electric Transmission Lines(Hindawi, 2014) Bamigbola, Olabode Matthias; Ali, Montaz M.; Awodele, Kehinde O.A modern and civilized society is so much dependent on the use of electrical energy because it has been the most powerful vehicle for facilitating economic, industrial, and social developments. Electrical energy produced at power stations is transmitted to load centres from where it is distributed to its consumers through the use of transmission lines run from one place to another. As a result of the physical properties of the transmission medium, some of the transmitted power is lost to the surroundings.The overall effect of power losses on the system is a reduction in the quantity of power available to the consumers. An accurate knowledge of transmission losses is hinged on the ability to correctly predict the available current and voltage along transmission lines.Therefore, mathematical physics expressions depicting the evolution of current and voltage on a typical transmission line were formulated, and derived therefrom were models to predict available current and voltage, respectively, at any point on the transmission line. The predictive models evolved as explicit expressions of the space variable and they are in close agreement with empirical data and reality.Item Pulse Vaccination Strategy in a SVEIRS Epidemic Model with Two-Time Delay and Saturated Incidence(Horizon Research Publishing, 2014) Bolarin, Gbolahan; Bamigbola, Olabode MatthiasFinding the best way to vaccinate people against infectious disease is an important issue for health workers. In this study a compartmental two-time delay SVEIRS mathematical model with pulse vaccination and saturated incidence was formulated to examine the dynamics of infectious disease in a population. The existence of the disease free periodic solution was established and the compact form was derived. From our study, it was discovered that short pulse vaccination or long latent period or long immune period will guarantee eradication of the disease in the population. Lastly, the conditions for the incurability of the disease were examined.Item A qualitative study of the optimal control model for an electric power generating system(South African Energy Research Center, 2012-05) Aderinto, Yidiat O.; Bamigbola, Olabode Matthias