We consider a primal-dual potential reduction algorithm for nonlinear convex optimization problems over symmetric cones. The same complexity estimates as in the case of linear objective function are obtained provided a certain nonlinear system of equations can be solved with a given accuracy. This generalizes the result of K. Kortanek, F. Potra and Y.Ye. We further introduce a generalized Nesterov-Todd direction and show how it can be used to achieve a required accuracy for a class ofnonlinear convex functions satifying scaling Lipschitz condition. This result is a far-reaching generalization of those of F. Potra, Y. Ye and J. Zhu. Finally, we show that a class of functions (which contains quantum entropy function) satisfies scaling Lipschitz condition

## Citation

Preprint, June 2016, Department of Mathematics, University of Notre Dame