A modified Newton method for unconstrained minimization

Technical Report · Sat Jul 01 00:00:00 EDT 1989

DOI:https://doi.org/10.2172/5453213· OSTI ID:5453213

Forsgren, A. L.; Gill, P. E.; Murray, W.

Newton's method has proved to be a very efficient method for solving strictly convex unconstrained minimization problems. For the nonconvex case, various modified Newton methods have been proposed. In this paper, a new modified Newton method is presented. The method is a linesearch method, utilizing the Cholesky factorization of a positive-definite portion of the Hessian matrix. The search direction is defined as a linear combination of a descent direction and a direction of negative curvature. Theoretical properties of the method are established and its behaviour is studied when applied to a set of test problems. 27 refs., 6 figs., 4 tabs.

• Research Organization: Stanford Univ., CA (USA). Systems Optimization Lab.
• Sponsoring Organization: USDOD; DOE/ER; GGUSTF; National Science Foundation (NSF); SENBTD
• DOE Contract Number: FG03-87ER25030
• OSTI ID: 5453213
• Report Number(s): SOL-89-12; ON: DE89017331; CNN: ECS-8715153; N00014-87-K-0142
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
MATRICES
FACTORIZATION
NEWTON METHOD
MODIFICATIONS
ALGORITHMS
CONVERGENCE
ITERATIVE METHODS
MATHEMATICAL LOGIC
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