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.


References in zbMATH (referenced in 79 articles )

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  1. Liu, Hongwei; Liu, Zexian: An efficient Barzilai-Borwein conjugate gradient method for unconstrained optimization (2019)
  2. Andrei, Neculai: A diagonal quasi-Newton updating method based on minimizing the measure function of Byrd and Nocedal for unconstrained optimization (2018)
  3. Andrei, Neculai: A double parameter scaled BFGS method for unconstrained optimization (2018)
  4. 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)
  5. Babaie-Kafaki, Saman; Ghanbari, Reza: A linear hybridization of the Hestenes-Stiefel method and the memoryless BFGS technique (2018)
  6. Dong, XiaoLiang; Han, Deren; Dai, Zhifeng; Li, Lixiang; Zhu, Jianguang: An accelerated three-term conjugate gradient method with sufficient descent condition and conjugacy condition (2018)
  7. Li, Ming; Liu, Hongwei; Liu, Zexian: A new family of conjugate gradient methods for unconstrained optimization (2018)
  8. Li, Ming; Liu, Hongwei; Liu, Zexian: A new subspace minimization conjugate gradient method with nonmonotone line search for unconstrained optimization (2018)
  9. Livieris, Ioannis E.; Tampakas, Vassilis; Pintelas, Panagiotis: A descent hybrid conjugate gradient method based on the memoryless BFGS update (2018)
  10. Li, Xiangrong; Wang, Xiaoliang; Sheng, Zhou; Duan, Xiabin: A modified conjugate gradient algorithm with backtracking line search technique for large-scale nonlinear equations (2018)
  11. Ou, Yigui: A note on the global convergence theorem of accelerated adaptive Perry conjugate gradient methods (2018)
  12. Ou, Yigui; Li, Jingya: A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints (2018)
  13. Ou, Yigui; Zhou, Xin: A modified scaled memoryless BFGS preconditioned conjugate gradient algorithm for nonsmooth convex optimization (2018)
  14. Sheng, Zhou; Yuan, Gonglin; Cui, Zengru: A new adaptive trust region algorithm for optimization problems (2018)
  15. Yao, Shengwei; He, Donglei; Shi, Lihua: An improved Perry conjugate gradient method with adaptive parameter choice (2018)
  16. Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma: Novel preconditioners based on quasi-Newton updates for nonlinear conjugate gradient methods (2017)
  17. Andrei, Neculai: Eigenvalues versus singular values study in conjugate gradient algorithms for large-scale unconstrained optimization (2017)
  18. Andrei, Neculai: Accelerated adaptive Perry conjugate gradient algorithms based on the self-scaling memoryless BFGS update (2017)
  19. Babaie-Kafaki, Saman; Ghanbari, Reza: A class of descent four-term extension of the Dai-Liao conjugate gradient method based on the scaled memoryless BFGS update (2017)
  20. Babaie-Kafaki, Saman; Ghanbari, Reza: A class of adaptive dai-liao conjugate gradient methods based on the scaled memoryless BFGS update (2017)

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