SCALCG
SCALCG – Scaled conjugate gradient algorithms for unconstrained optimization. In this work we present and analyze a new scaled conjugate gradient algorithm and its implementation, based on an interpretation of the secant equation and on the inexact Wolfe line search conditions. The best spectral conjugate gradient algorithm SCG by Birgin and Martínez (2001), which is mainly a scaled variant of Perry’s (1977), is modified in such a manner to overcome the lack of positive definiteness of the matrix defining the search direction. This modification is based on the quasi-Newton BFGS updating formula. The computational scheme is embedded in the restart philosophy of Beale–Powell. The parameter scaling the gradient is selected as spectral gradient or in an anticipative manner by means of a formula using the function values in two successive points. In very mild conditions it is shown that, for strongly convex functions, the algorithm is global convergent. Preliminary computational results, for a set consisting of 500 unconstrained optimization test problems, show that this new scaled conjugate gradient algorithm substantially outperforms the spectral conjugate gradient SCG algorithm.
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Sorted by year (- Andrei, Neculai: A double parameter self-scaling memoryless BFGS method for unconstrained optimization (2020)
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- Dehghani, R.; Mahdavi-Amiri, N.: Scaled nonlinear conjugate gradient methods for nonlinear least squares problems (2019)
- Faramarzi, Parvaneh; Amini, Keyvan: A modified spectral conjugate gradient method with global convergence (2019)
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- Liu, Hongwei; Liu, Zexian: An efficient Barzilai-Borwein conjugate gradient method for unconstrained optimization (2019)
- Liu, J. K.; Feng, Y. M.; Zou, L. M.: A spectral conjugate gradient method for solving large-scale unconstrained optimization (2019)
- Rezaee, Saeed; Babaie-Kafaki, Saman: An adaptive nonmonotone trust region method based on a modified scalar approximation of the Hessian in the successive quadratic subproblems (2019)
- Xue, Yanqin; Liu, Hongwei; Liu, Zexian: An improved nonmonotone adaptive trust region method. (2019)
- Andrei, Neculai: A double-parameter scaling Broyden-Fletcher-Goldfarb-Shanno method based on minimizing the measure function of Byrd and Nocedal for unconstrained optimization (2018)