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Higher Order Iteration Schemes for Unconstrained Optimization

Author(s): Yangyang Shi | Pingqi Pan

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 01;
Issue: 03;
Start page: 73;
Date: 2011;
Original page

Keywords: Unconstrained Optimization | Iteration Scheme | ODE Method | Quasi-Newton Update | Convergence Analysis

Using a predictor-corrector tactic, this paper derives new iteration schemes for unconstrained optimization. It yields a point (predictor) by some line search from the current point; then with the two points it constructs a quadratic interpolation curve to approximate some ODE trajectory; it finally determines a new point (corrector) by searching along the quadratic curve. In particular, this paper gives a global convergence analysis for schemes associated with the quasi-Newton updates. In our computational experiments, the new schemes using DFP and BFGS updates outperformed their conventional counterparts on a set of standard test problems.

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