STENMIN: A software package for large, sparse unconstrained optimization using tensor methods

We describe a new package for minimizing an unconstrained nonlinear function where the Hessian is large and sparse. The software allows the user to select between a tensor method and a standard method based upon a quadratic model. The tensor method models the objective function by a fourth-order model, where the third- and fourth-order terms are chosen such that the extra cost of forming and solving the model is small. The new contribution of this package consists of the incorporation of an entirely new way of minimizing the tensor model that makes it suitable for solving large, sparse optimization problems efficiently. The test results indicate that, in general, the tensor method is significantly more efficient and more reliable than the standard Newton method for solving large, sparse unconstrained optimization problems. 12 refs., 1 tab