Solution of Quadratic Programming with Interval Variables Using a Two-Level Programming Approach

Syaripuddin Syaripuddin,Fatmawati Fatmawati,Herry Suprajitno

doi:10.1155/2018/5204375

Syaripuddin Syaripuddin, Fatmawati Fatmawati + Show 1 more

Open Access

https://doi.org/10.1155/2018/5204375

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Abstract

Quadratic programming with interval variables is developed from quadratic programming with interval coefficients to obtain optimum solution in interval form, both the optimum point and optimum value. In this paper, a two-level programming approach is used to solve quadratic programming with interval variables. Procedure of two-level programming is transforming the quadratic programming model with interval variables into a pair of classical quadratic programming models, namely, the best optimum and worst optimum problems. The procedure to solve the best and worst optimum problems is also constructed to obtain optimum solution in interval form.

Highlights

Classic quadratic programming requires the assumption that the coefficient value is certainly known
The uncertain coefficient value can be estimated using intervals based on the theory of interval analysis which is developed by Moore [1]
The special characteristic of the interval quadratic programming is the coefficients and variables of the objective functions and constraints are in interval form

Summary

Introduction

Classic quadratic programming requires the assumption that the coefficient value is certainly known. Reference [8] presented procedures to obtain optimum solution in interval form for both optimum point and optimum value. Journal of Applied Mathematics the coefficients and variables in the linear programming in the interval form and constructed a solution by using a two-level programming approach with some additional procedures for obtaining an interval solution. This paper discusses the solution of quadratic programming with interval variables using a two-level programming approach that focuses on how to obtain the optimum solution in interval form, for both optimum point and optimum value. The last step is constructing the procedure of interval solution in the classic quadratic programming model by adding new constraints to the model which has unbounded solution in order to restrict the feasible area.

Interval Arithmetic

Quadratic Programming with Interval Coefficient

Quadratic Programming with Interval Variable

Two-Level Programming

Numerical Example

Conclusion