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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 52, 2003 - Issue 4-5
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Original Articles

Alternate step gradient methodFootnote*

Pages 395-415 | Received 26 Nov 2002, Accepted 23 Jul 2003, Published online: 13 May 2010

References

  • Akaike , H. 1959 . On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method . Ann. Inst. Statist. Math. Tokyo , 11 : 1 – 17 .
  • Birgin , E.G. , Chambouleyron , I. and Martínez , J.M. 1999 . Estimation of the optical constants and the thickness of thin films using unconstrained optimization . J. Comput. Phys. , 151 : 862 – 880 .
  • Birgin , E.G. , Martínez , J.M. and Raydan , M. 2000 . Nonmonotone spectral projected gradient methods on convex sets . SIAM J. Optim. , 10 : 1196 – 1211 .
  • Barzilai , J. and Borwein , J.M. 1988 . Two-point step size gradient methods . IMA J. Numer. Anal. , 8 : 141 – 148 .
  • Cauchy , A. 1847 . Méthode générale pour la résolution des systéms d’équations simultanées . Comp. Rend. Sci. Paris , 25 : 536 – 538 .
  • Dai , Y.H. 2002 . On the nonmonotone line search . Journal of Optimization Theory and Applications , 112 ( 2 ) : 315 – 330 .
  • Dai , Y.H. and Liao , L.-Z. 2002 . R -linear convergence of the Barzilai and Borwein gradient method . IMA J. Numer. Anal. , 22 : 1 – 10 .
  • Dai Y.H. Yuan J.Y. 2001 On a class of gradient algorithms for unconstrained optimization (Preprint)
  • Fletcher , R. 1999 . Low storage methods for unconstrained optimization . Lectures in Applied Mathematics (AMS) , 26 : 165 – 179 .
  • Fletcher R. 2001 The Barzilai Borwein Method – Steepest Descent Resurgent? Report in the International Workshop on Optimization and Control with Applications July 9–17 Erice Italy
  • Fletcher , R. and Reeves , C. 1964 . Function minimization by conjugate gradients . Comput. J. , 7 : 149 – 154 .
  • Friedlander , A. , Martínez , J.M. , Molina , B. and Raydan , M. 1999 . Gradient method with retards and generalizations . SIAM J. Numer. Anal. , 36 : 275 – 289 .
  • Glunt , W. , Hayden , T.L. and Raydan , M. 1993 . Molecular conformations from distance matrices . J. Comput. Chem. , 14 : 114 – 120 .
  • Grippo , L. , Lampariello , F. and Lucidi , S. 1986 . A nonmonotone line search technique for Newton's method . SIAM J. Numer. Anal. , 23 : 707 – 716 .
  • Hestenes , M.R. and Stiefel , E.L. 1952 . Methods of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Standards Sect. , 5 ( 49 ) : 409 – 436 .
  • Lai , Y.L. 1981 . Some properties of the steepest descent method . Acta Mathematicae Applicatae Sinica , 4 ( 2 ) : 106 – 116 .
  • Liu , W.B. and Dai , Y.H. 2001 . Minimization algorithms based on supervisor and searcher cooperation . Journal of Optimization Theory and Applications , 111 ( 2 ) : 359 – 379 .
  • Moré , J.J. , Garbow , B.S. and Hillstrom , K.E. 1981 . Testing unconstrained optimization software . ACM Transactions on Mathematical Software , 7 : 17 – 41 .
  • Nocedal , J. , Sartentaer , A. and Zhu , C. 2002 . On the behavior of the gradient norm in the steepest descent method . Computational Optimization and Applications , 22 ( 1 ) : 5 – 35 .
  • Raydan , M. 1993 . On the Barzilai and Borwein choice of steplength for the gradient method . IMA J. Numer. Anal. , 13 : 321 – 326 .
  • Raydan , M. 1997 . The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem . SIAM J. Optim. , 7 : 26 – 33 .
  • Raydan M. 2001 Nonmonotone spectral methods for large-scale nonlinear systems Report in the International Workshop on Optimization and Control with Applications July 9–17 Erice Italy

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