Applying a Newton Method to Strictly Convex Separable Network Quadratic Programs

Introduction This paper describes the application of Newton Method for solving strictly convex separable network quadratic programs. The authors provide a brief synopsis of separable network quadratic programming and list the various techniques for solving the same. The main thrust of the paper is succinctly identified by the following: 1. Providing a generic subroutine that can be used by various existing techniques to handle non-smooth piecewise quadratic cost functions. 2. Testing the use of quadratic penalty functions in context of network programming. 3. Performance of their non-smooth Newton method for solving network quadratic programming Newton’s direction achieves a quadratic convergence when the iterates are close to the optimal solution. However, as the paper points out, the calculation of exact Newton direction is very expensive and may be prohibitive for large scale separable network quadratic programs. So the authors propose an iterative solution for computing approximate Newton direction and provide detailed bounds on the running time and complexity of the iterative algorithm.