American Journal of Operations Research

Volume 1, Issue 3 (September 2011)

ISSN Print: 2160-8830   ISSN Online: 2160-8849

Google-based Impact Factor: 0.84  Citations  

Higher Order Iteration Schemes for Unconstrained Optimization

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DOI: 10.4236/ajor.2011.13011    6,314 Downloads   10,769 Views  Citations

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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.

Share and Cite:

Y. Shi and P. Pan, "Higher Order Iteration Schemes for Unconstrained Optimization," American Journal of Operations Research, Vol. 1 No. 3, 2011, pp. 73-83. doi: 10.4236/ajor.2011.13011.

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