Monotone limits in linear programming problems

The aim of this paper is to investigate the behavior of values of linear programming problems under some monotone variations of objective functions and constraints. More precisely, let X and Y be real linear spaces paired under the bilinear functional ((,))i, and let Z and W be real linear spaces paired under the bilinear functional ( ( , ) ) 2 A (linear) program for these paired spaces is a quintuple (A, P, Q, j 0 ? z0). In this quintuple, A is a linear transformation from X into Z, P is a convex cone in X, Q is a convex cone in Z, γ0 is an element of Y and z0 is an element of Z. The set S of feasible solutions for the program and the value M of the program are defined by