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K. J. Arrow, L. Hurwicz and H. Uzawa, “Studies in Linear and Nonlinear Programming,” Stanford University Press, Palo Alto, 1958.

has been cited by the following article:

• 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.