Truncated Newton Algorithm

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See: Newton's Algorithm, L-BFGS, Iterative Scaling.



    • QUOTE: Truncated Newton methods were introduced in the early 1980s [18] and have since been gaining popularity. They are based on the idea that an exact solution of the Newton equation at every step is unnecessary and can be computationally wasteful in the framework of a basic descent method. Any descent direction will suffice when the objective function is not well approximated by a convex quadratic and, as a solution to the minimization problem is approached, more effort in solution of the Newton equation may be warranted. Their appeal to scientific applications is their ability to exploit function structure to accelerate convergence.


  • Dembo, R.S. and Steihaug, T., Truncated-Newton Algorithms for Large-Scale Unconstrained Optimization, Math. Prog. 26, 190-212 (1983). [ Advanced article presenting the truncated Newton method in theoretical detail.]