On the relationship between the integer and continuous solutions of convexprograms

A bound is obtained in this note for the distance between the integer and r eal solutions to convex quadratic programs. This bound is a function of the condition number of the Hessian matrix. We further extend this proximity r esult to convex programs and mixed-integer convex programs. We also show th at this bound is achievable in certain situations and the distance between the integer and continuous minimizers may tend to infinity. (C) 2001 Elsevi er Science B.V. All rights reserved.