Network constraints occur commonly in optimization. They arise because network themselves are a common feature of models. The network is used to describe such infrastructure as a gas network, the web, public highways, etc. Network constraints arise within an optimization problem when one seeks the optimal flow of goods, water, electrical current, etc on a network. To date, the focus of most research on optimization algorithms for problems with network constraints has been in conjunction with a linear objective. Little work has been done with nonlinear and non-convex objective. That is the problem we address. We present a new algorithm based on a primal-dual method in which the sub-problems are solved using a null-space approach combined with a truncated conjugate-gradient algorithm. When necessary, a direction of negative curvature is also computed.; We have created a new test set of test problems by combining a set of objective available in the public domain with a set of network constraints. Results of our algorithm on the test set are presented.
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