
Tensor methods for large, sparse unconstrained optimization
Author(s) -
Ali Bouaricha
Publication year - 1996
Language(s) - English
Resource type - Reports
DOI - 10.2172/409872
Subject(s) - hessian matrix , tensor (intrinsic definition) , invertible matrix , optimization problem , mathematics , mathematical optimization , computer science , constrained optimization problem , algorithm , pure mathematics
Tensor methods for unconstrained optimization were first introduced by Schnabel and Chow [SIAM J. Optimization, 1 (1991), pp. 293-315], who describe these methods for small to moderate size problems. This paper extends these methods to large, sparse unconstrained optimization problems. This requires an entirely new way of solving the tensor model that makes the methods suitable for solving large, sparse optimization problems efficiently. We present test results for sets of problems where the Hessian at the minimizer is nonsingular and where it is singular. These results show that tensor methods are significantly more efficient and more reliable than standard methods based on Newton`s method