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Higher Order Iteration Schemes for Unconstrained Optimization

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DOI: 10.4236/ajor.2011.13011    5,614 Downloads   9,559 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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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