Tensor methods for large, sparse unconstrained optimization
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.
- Research Organization:
- Argonne National Lab., IL (United States). Mathematics and Computer Science Div.
- Sponsoring Organization:
- USDOE Office of Energy Research, Washington, DC (United States)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 409872
- Report Number(s):
- MCS-P--452-0794; ON: DE97001016
- Country of Publication:
- United States
- Language:
- English
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