Error bounds for the aggregated convex programming problem

Applied mathematical programming problems are often approximations of larger, more detailed problems. One criterion to evaluate an approximating program is the magnitude of the difference between the optimal objective values of the original and the approximating program. The approximation we consider is variable aggregation in a convex program. Bounds are derived on the difference between the two optimal objective values. Previous results of Geoffrion and Zipkin are obtained by specializing our results to linear programming. Also, we apply our bounds to a convex transportation problem.