A New Approach for Kuhn-Tucker Conditions to Solve Quadratic Programming Problems with Linear Inequality Constraints
Ayansola Olufemi Aderemi,
Adejumo Adebowale Olusola
Issue:
Volume 5, Issue 5, September 2020
Pages:
86-92
Received:
27 May 2020
Accepted:
18 September 2020
Published:
11 December 2020
Abstract: Many real-life problems, such as economic, industrial, engineering to mention but a few has been dealt with, using linear programming that assumes linearity in the objective function and constraint functions. It is noteworthy that there are many situations where the objective function and / or some or all of the constraints are non-linear functions. It is observed that many researchers have laboured so much at finding general solution approach to Non-linear programming problems but all to no avail. Of the prominent methods of solution of Non-linear programming problems: Karush- Kuhn-Tucker conditions method and Wolf modified simplex method. The Karush-Kuhn-Tucker theorem gives necessary and sufficient conditions for the existence of an optimal solution to non-linear programming problems, a finite-dimensional optimization problem where the variables have to fulfill some inequality constraints while Wolf in addition to Karush- Kuhn-Tucker conditions, modified the simplex method after changing quadratic linear function in the objective function to linear function. In this paper, an alternative method for Karush-Kuhn-Tucker conditional method is proposed. This method is simpler than the two methods considered to solve quadratic programming problems of maximizing quadratic objective function subject to a set of linear inequality constraints. This is established because of its computational efforts.
Abstract: Many real-life problems, such as economic, industrial, engineering to mention but a few has been dealt with, using linear programming that assumes linearity in the objective function and constraint functions. It is noteworthy that there are many situations where the objective function and / or some or all of the constraints are non-linear functions...
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Modelling and Analysis of Effect of Awareness Programs by Media on the Spread of COVID-19 Pandemic Disease
Issue:
Volume 5, Issue 5, September 2020
Pages:
93-102
Received:
21 October 2020
Accepted:
4 November 2020
Published:
11 December 2020
Abstract: This paper proposes and analyses a basic deterministic mathematical model to investigate Modeling and Analysis of effect of awareness program by media on the spread COVID-19 Pandemic Disease. The model has seven non-linear differential equations, which describe the effects of awareness programs by media on the spread of COVID-19 Pandemic diseases. Analytical study carried out to investigate the model analysis and existence of stability of system, given threshold parameters known as the basic reproduction number, which obtained using next generation matrix method. The equilibrium of COVID 19 models is determined. In addition to having a disease-free equilibrium, which is globally asymptotically stable when the basic reproduction number less than one, COVID 19 model manifest one's possession of (a quality of) the phenomenon of backward bifurcation where a stable disease-free equilibrium co-exists (at the same time) with a stable endemic equilibrium for a certain range of associated reproduction number less than one. The analysis and simulation results of the model suggested that the most effective strategies for controlling or eradicating the spread of COVID 19 pandemic were suggest using that awareness programs through the media campaigning are helpful in decreasing the spread of COVID 19 Pandemic diseases by isolating a fraction of susceptible from infective.
Abstract: This paper proposes and analyses a basic deterministic mathematical model to investigate Modeling and Analysis of effect of awareness program by media on the spread COVID-19 Pandemic Disease. The model has seven non-linear differential equations, which describe the effects of awareness programs by media on the spread of COVID-19 Pandemic diseases. ...
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