Abstract
In this paper we combine a secant method with a trust region strategy so that the resulting algorithm not only has a local two-step superlinear rate, but also globally converges to Karush-Kuhn-Tucker points. The condition for proving these convergence properties is weaker than some trust region methods which use reduced Hessian as a tool. A minor revision of this algorithm is shown to possess a one-step superlinear rate.
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The authors gratefully acknowledge the partial support of City Polytechnic of Hong Kong (Grant 700126).
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Zhang, J., Zhu, D. A convergent secant method for constrained optimization. Japan J. Indust. Appl. Math. 11, 265–288 (1994). https://doi.org/10.1007/BF03167225
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DOI: https://doi.org/10.1007/BF03167225