Linping Sun
		Key words:
		unconstrained optimization, quasi-Newton, rank-one update, optimal condition, convergence, finite termination, large scale, limited memory, preconditioned conjugate gradient, derivative-free
		Mathematices Subject Classification: 49M37, 65K05, 90C30

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	Abstract:
	A stabilized version of the symmetric rank-one updating method is developed for unconstrained optimization. The basic feature of the method is that they can ensure the positive definiteness of the successive estimates to the inverse Hessian while satisfying Davidon's optimal condition automatically. Numerical results show that the method, which is called as OCSSR1 method, compares favorably with good implementations of other existing methods. In this contribution, we give an extensive review of the OCSSR1 algorithm and its possible extensions on various aspects.

An approach to scaling symmetric rank-one update

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Special Issue on Conjugate Gradient and Quasi-Newton Methods for Nonlinear Optimization
Volume 2, Number 1, January 2006, pp. 105-118