Robust Basis of Interval Multiobjective Linear and Quadratic Programming

Abstract

In this paper we deal with multiobjective linear and quadratic programming problem with uncertain information. So far in the field of statistical analysis and data mining, e.g., mean-variance portfolio problem, support vector machine and their varieties, we have encountered various kinds of quadratic and linear programming problems with multiple criteria. Moreover coefficients in such problems have uncertainty that is expressed by interval, probabilistic distribution or possibilistic (fuzzy) distribution. In this paper, we define a robust basis for all possible perturbation of coefficients within intervals in objective functions and constraints that is regarded as secure and conservative solution under uncertainty. According to the conventional multi-objective programming literature, it is required to solve test subproblem for each basis. Therefore, in case of our interval problem excessive computational demand is estimated. In this paper investigating the properties of robust basis by means of combination of interval extreme points we obtained the result that the robust basis can be examined by working with only a finite subset of possible perturbations of the coefficients