# Sparse Hessian Factorization in Curved Trajectories for Unconstrained Minimization

### Al Jimenez, Cal Poly, Mathematics Dept.

### Abstract:

The Curved Trajectories Algorithm (CTA) for the minimization of unconstrained functions of several variables follows polynomial space curves at each step. The space curves result from truncations of a Taylor series expansion of the solution. A critical step in the efficiency of CTA is the factorization of the sparse hessian matrix and handling a non positive hessian. This paper describes a new approach for non-positive hessians that has given robust results that compare very favorably with other minimization algorithms using a sample of the Cuter problems.