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All issues Volume 56 / No 4 (July-August 2022) RAIRO-Oper. Res., 56 4 (2022) 2403-2424 References
Open Access
Issue
RAIRO-Oper. Res.
Volume 56, Number 4, July-August 2022
Page(s) 2403 - 2424
DOI https://doi.org/10.1051/ro/2022107
Published online 01 August 2022
  • H. Akaike, On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method. Ann. Inst. Statist. Math. 11 (1959) 1–17. [CrossRef] [MathSciNet] [Google Scholar]
  • N. Andrei, An unconstrained optimization test functions collection. Adv. Model. Optim. 10 (2008) 147–161. [MathSciNet] [Google Scholar]
  • J. Barzilai and J.M. Borwein, Two-point step size gradient methods. IMA J. Numer. Anal. 8 (1988) 141–148. [CrossRef] [MathSciNet] [Google Scholar]
  • T. Bianconcini and M.Q. Sciandrone, A cubic regularization algorithm for unconstrained optimization using line search and nonmonotone techniques. Optim. Methods Softw. 31 (2016) 1008–1035. [CrossRef] [MathSciNet] [Google Scholar]
  • T. Bianconcini, G. Liuzzi and B. Morini, On the use of iterative methods in cubic regularization for unconstrained optimization. Comput. Optim. Appl. 60 (2015) 35–57. [CrossRef] [MathSciNet] [Google Scholar]
  • F. Biglari and M. Solimanpur, Scaling on the spectral gradient method. J. Optim. Theory Appl. 158 (2013) 626–635. [CrossRef] [MathSciNet] [Google Scholar]
  • E.G. Birgin, J.M. Martínez and M. Raydan, Nonmonotone spectral projected gradient methods for convex sets. SIAM J. Optim. 10 (2000) 1196–1211. [CrossRef] [MathSciNet] [Google Scholar]
  • C. Cartis, N.I.M. Gould and P.L. Toint, Adaptive cubic regularisation methods for unconstrained optimization. Part I: motivation, convergence and numerical results. Math. Program. 127 (2011) 245–295. [CrossRef] [MathSciNet] [Google Scholar]
  • C. Cartis, N.I. Gould and P.L. Toint, Adaptive cubic regularisation methods for unconstrained optimization. Part II: worst-case function-and derivative-evaluation complexity. Math. Program. 130 (2011) 295–319. [CrossRef] [MathSciNet] [Google Scholar]
  • A. Cauchy, Méthode générale pour la résolution des systéms déquations simultanées. Comput. Rend. Sci. Paris 25 (1847) 46–89. [Google Scholar]
  • Y.H. Dai and C.X. Kou, A nonlinear conjugate gradient algorithm with an optimal property and an improved Wolfe line search. SIAM J. Optim. 23 (2013) 296–320. [Google Scholar]
  • Y.H. Dai and L.Z. Liao, R-linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. 22 (2002) 1–10. [CrossRef] [MathSciNet] [Google Scholar]
  • Y.H. Dai and H.C. Zhang, An adaptive two-point stepsize gradient algorithm. Numer. Algorithms 27 (2001) 377–385. [CrossRef] [MathSciNet] [Google Scholar]
  • Y.H. Dai, J.Y. Yuan and Y.X. Yuan, Modified two-point stepsize gradient methods for unconstrained optimization. Comput. Optim. Appl. 22 (2002) 103–109. [CrossRef] [MathSciNet] [Google Scholar]
  • Y.H. Dai, W.W. Hager, K. Schittkowski and H. Zhang, The cyclic Barzilai-Borwein method for unconstrained optimization. IMA J. Numer. Anal. 26 (2006) 604–627. [CrossRef] [MathSciNet] [Google Scholar]
  • E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201–213. [Google Scholar]
  • N.I.M. Gould and M. Porcelli, Updating the regularization parameter in the adaptive cubic regularization algorithm. Comput. Optim. Appl. 53 (2012) 1–22. [CrossRef] [MathSciNet] [Google Scholar]
  • N.I.M. Gould, D. Orban and P.L. Toint, CUTEr and SifDec: a constrained and unconstrained testing environment, revisited. ACM Trans. Math. Softw. 29 (2003) 373–394. [Google Scholar]
  • L. Grippo, F. Lamparillo and S. Lucidi, A nonmonotone line search technique for Newton’s method. SIAM J. Numer. Anal. 23 (1986) 707–716. [CrossRef] [MathSciNet] [Google Scholar]
  • W.W. Hager and H.C. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM J. Optim. 16 (2005) 170–192. [CrossRef] [Google Scholar]
  • W.W. Hager and H.C. Zhang, Algorithm 851: CG_DESCENT, a conjugate gradient method with guaranteed descent. ACM Trans. Math. Softw. 32 (2006) 113–137. [CrossRef] [Google Scholar]
  • Y.K. Huang, Y.H. Dai and X.W. Liu, Equipping Barzilai-Borwein method with two dimensional quadratic termination property. SIAM J. Optim. 31 (2021) 3068–3096. [CrossRef] [MathSciNet] [Google Scholar]
  • D.W. Li and R.Y. Sun, On a faster R-linear convergence rate of the Barzilai-Borwein method (2020). Preprint arXiv:2101.00205. [Google Scholar]
  • Z.X. Liu and H.W. Liu, Several efficient gradient methods with approximate optimal stepsizes for large scale unconstrained optimization. J. Comput. Appl. Math. 328 (2018) 400–413. [CrossRef] [MathSciNet] [Google Scholar]
  • Z.X. Liu and H.W. Liu, An efficient gradient method with approximate optimal stepsize for large-scale unconstrained optimization. Numer. Algorithms 78 (2018) 21–39. [CrossRef] [MathSciNet] [Google Scholar]
  • Z.X. Liu, H.W. Liu and X.L. Dong, An efficient gradient method with approximate optimal stepsize for the strictly convex quadratic minimization problem. Optimization 67 (2018) 427–440. [CrossRef] [MathSciNet] [Google Scholar]
  • F. Luengo and M. Raydan, Gradient method with dynamical retards for large-scale optimization problems. Electron. Trans. Numer. Anal. 16 (2003) 186–193. [MathSciNet] [Google Scholar]
  • M. Miladinović, P. Stanimirović and S. Miljković, Scalar correction method for solving large scale unconstrained minimization problems. J. Optim. Theory Appl. 151 (2011) 304–320. [CrossRef] [MathSciNet] [Google Scholar]
  • H. Nosratipour, O.S. Fard and A.H. Borzabadi, An adaptive nonmonotone global Barzilai-Borwein gradient method for unconstrained optimization. Optimization 66 (2017) 641–655. [CrossRef] [MathSciNet] [Google Scholar]
  • M. Raydan and On the Barzilai and Borwein choice of steplength for the gradient method. IMA J. Numer. Anal. 13 (1993) 321–326. [CrossRef] [MathSciNet] [Google Scholar]
  • M. Raydan, The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem. SIAM J. Optim. 7 (1997) 26–33. [Google Scholar]
  • W.Y. Sun, Optimization methods for non-quadratic model. Asia-Pac. J. Oper. Res. 13 (1996) 43–63. [Google Scholar]
  • W.Y. Sun and D. Xu, A filter-trust-region method based on conic model for unconstrained optimization. Sci. Sin. Math. 55 (2012) 527–543. [Google Scholar]
  • P.L. Toint, A non-monotone trust-region algorithm for nonlinear optimization subject to convex constraints. Math. Program. 77 (1997) 69–94. [Google Scholar]
  • Y.H. Xiao, Q.Y. Wang and D. Wang, Notes on the Dai-Yuan-Yuan modified spectral gradient method. J. Comput. Appl. Math. 234 (2010) 2986–2992. [CrossRef] [MathSciNet] [Google Scholar]
  • Y.X. Yuan, A new stepsize for the steepest descent method. J. Comput. Math. 24 (2006) 149–156. [MathSciNet] [Google Scholar]
  • H.C. Zhang and W.W. Hager, A nonmonotone line search technique and its application to unconstrained optimization. SIAM J. Optim. 14 (2004) 1043–1056. [CrossRef] [MathSciNet] [Google Scholar]
  • J.Z. Zhang, N.Y. Deng and L.H. Chen, New quasi-Newton equation and related methods for unconstrained optimization. J. Optim. Theory Appl. 102 (1999) 147–167. [Google Scholar]

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