Computing modified Newton directions using a partial Cholesky factorization
- Royal Inst. of Tech., Stockholm (Sweden). Dept. of Mathematics
- Univ. of California, San Diego, La Jolla, CA (United States). Dept. of Mathematics
- Stanford Univ., CA (United States). Dept. of Operations Research
The effectiveness of Newton's method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton methods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that satisfy the second-order necessary conditions for optimality. The authors propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial Cholesky factorization of the Hessian. This factorization not only gives theoretically satisfactory directions, but also requires only a partial pivoting strategy; i.e., the equivalent of only two rows of the Schur complement needs to be examined at each step.
- DOE Contract Number:
- FG03-92ER25117
- OSTI ID:
- 6560352
- Journal Information:
- SIAM Journal on Scientific Computing; (United States), Journal Name: SIAM Journal on Scientific Computing; (United States) Vol. 16:1; ISSN 1064-8275; ISSN SJOCE3
- Country of Publication:
- United States
- Language:
- English
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