Parameterized solution of linear interval parametric systems

Let A(p)x=b(p),p∈p denote a linear interval parametric system whose elements aij(p) and bi(p) are given functions of the entries of the parameter vector p. In this paper, a new type of solution x(p) of the parametric system considered is suggested. The new solution x(p) is of the form x(p)=Lp+a,p∈p where L is a real n×m matrix (n and m are the sizes of the square matrix A and vector p, respectively) whereas a is an interval vector. It is shown that the parameterized solution can be employed for solving various constrained optimization problems related to the linear interval parametric system given. Thus, an iterative method for determining the interval hull solution of A(p)x=b(p),p∈p for the case of linear parametric dependencies has been proposed which is based on the use of x(p) and a simple constraint satisfaction technique.