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A New Approach for Kuhn-Tucker Conditions to Solve Quadratic Programming Problems with Linear Inequality Constraints
Mathematics and Computer Science
Volume 5, Issue 5, September 2020, Pages: 86-92
Received: May 27, 2020; Accepted: Sep. 18, 2020; Published: Dec. 11, 2020
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Authors
Ayansola Olufemi Aderemi, Department of Mathematics & Statistics, The Polytechnic Ibadan, Ibadan, Nigeria
Adejumo Adebowale Olusola, Department of Statistics, University of Ilorin, Ilorin, Nigeria
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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.
Keywords
Karush- Kuhn-Tucker Conditions, New Approach, Quadratic Programming, Wolf Modified Simplex Method
To cite this article
Ayansola Olufemi Aderemi, Adejumo Adebowale Olusola, A New Approach for Kuhn-Tucker Conditions to Solve Quadratic Programming Problems with Linear Inequality Constraints, Mathematics and Computer Science. Vol. 5, No. 5, 2020, pp. 86-92. doi: 10.11648/j.mcs.20200505.11
Copyright
Copyright © 2020 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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