Refined proximity and sensitivity results in linearly constrained convex separable integer programming

Abstract

We define a new measure of the structure of a linear constraint matrix and establish some propertie. We then use the measure to refine proximity and sensitivity results in the literature. In particular, we refine bounds on the distance between continuous and discrete optima of linearly constrained convex separable programming problems and on the size of the feasible region for a linear program. We apply the results to improve the computational complexity of Hochbaum and Shanthikumar's algorithm for integer nonlinear programming, reducing the computational effort for certain problems from exponential to polynomial.