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Sparse Hessian Factorization in Curved Trajectories for Unconstrained Minimization

Al Jimenez, Cal Poly, Mathematics Dept.


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.