An Algorithm for Non-Linear Network Programming: Implementation, Results and Comparisons

Abstract

This paper evaluates an algorithm for solving network flow optimization problems with quadratic cost functions. Strategies for fast implementation are discussed and the results of extensive numerical tests are given. The performance of the algorithm measured by CPU time is compared with that of the convex simplex method specialized for quadratic network programming. Performance of the two methods is analysed with respect to network size and density, and other parameters of interest. The algorithm is shown to perform significantly better on the majority of problems. We also show how the algorithm may be used to solve non-linear convex network optimization problems by the use of sequential quadratic programming.

Keywords:

• Network Optimization
• Quadratic Programming
• Non-Linear Optimization
• Out-of-Kilter Algorithm
• Active Set Methods