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.
Highlights
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
Wolfe Philip [3] introduced a method for solving quadratic programming problems by modifying the simplex method to solve quadratic programming problems using in addition to it; Karush-Kuhn-Tucker conditions and changing the quadratic objective function into a linear objective function
Wolfe (1959) introduced Wolfe Modified Simplex Method where two phase simplex method are being modified and transforms of quadratic objective function into linear objective function is made necessary to solve non-linear programming problems having satisfy the requirement or conditions of Karush-Kuhn-Tucker theorem
Summary
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. In cases of large production in the product mix problems; the price of a product depends on the quantity demanded as the more the volume of sales; the lesser the price per unit These situations call for quadratic or non-linear programming formulation. Wolfe Philip [3] introduced a method for solving quadratic programming problems by modifying the simplex method to solve quadratic programming problems using in addition to it; Karush-Kuhn-Tucker conditions and changing the quadratic objective function into a linear objective function. A proposed algorithm and two of the existing methods vis-a-viz: Kuhn-Tucker condition and simplex like pivoting procedures called Wolf modified simplex method were employed to solve numerically a maximization problem of quadratic programming type if the objective function is non-linear and with linear inequality constraints
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