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An only 2-step \(Q\)-superlinear convergence example for some algorithms that use reduced Hessian approximations. (English) Zbl 0565.90060

It is shown by example that the reduced Hessian method for constrained optimization that is known to give 2-step \(Q\)-superlinear convergence may not converge \(Q\)-superlinearly.
Reviewer: Yaxiang Yuan

MSC:

90C30 Nonlinear programming
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
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References:

[1] R.H. Byrd, ”An example of irregular convergence in some constrained optimization methods that use the projected Hessian”,Mathematical Programming, this issue. · Zbl 0576.90079
[2] J. Goodman, ”Newton’s method for constrained optimization”, Courant Institute of Mathematical Sciences, New York University, New York (1982). · Zbl 0589.90065
[3] J. Nocedal and M. Overton, ”Projected Hessian updating algorithms for nonlinear constrained optimization” Report 59, Computer Science Department, New York University, New York (1983). · Zbl 0593.65043
[4] M. Overton, personal communication, 1984.
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[6] J. Stoer, ”Foundations of recursive quadratic programming methods for solving nonlinear programs”, Institut für Angewandte Mathematik und Statitik, Universität Würzburg, West Germany, presented at the NATO ASI on Computational Mathematical Programming, Bad Windsheim, West Germany (1984).
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