TITLE:
Higher Order Iteration Schemes for Unconstrained Optimization
AUTHORS:
Yangyang Shi, Pingqi Pan
KEYWORDS:
Unconstrained Optimization, Iteration Scheme, ODE Method, Quasi-Newton Update, Convergence Analysis
JOURNAL NAME:
American Journal of Operations Research,
Vol.1 No.3,
September
30,
2011
ABSTRACT: 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.