Hybridization of accelerated gradient descent method

1. Andrei, N: An acceleration of gradient descent algorithm with backtracking for unconstrained optimization. Numer. Algor. 42, 63–73 (2006)

   Article  MathSciNet  Google Scholar 

2. Andrei, N.: An unconstrained optimization test functions collection. http://www.ici.ro/camo/journal/vol10/v10a10.pdf

3. Armijo, L: Minimization of functions having Lipschitz first partial derivatives. Pac. J. Math. 6, 1–3 (1966)

   Article  MathSciNet  Google Scholar 

4. Bauschke, H., Combettes, P. L.: Convex analysis and monotone operator theory in Hilbert spaces, p 144. Springer, Berlin (2011)

   Book  Google Scholar 

5. Clarkson, J.A.: Uniformly convex spaces. Trans. Am. Math. Soc. 40, 396–414 (1936)

   Article  MathSciNet  Google Scholar 

6. Dai, Y.H., Liao, L.Z: R-linear convergence of the Barzilai and Borwein gradient method. IMA J. Numer. Anal. 22, 1–10 (2002)

   Article  MathSciNet  Google Scholar 

7. Fletcher, R., Reeves, C.M.: Function minimization by conjugate gradients. Comput. J. 7, 149–154 (1964)

   Article  MathSciNet  Google Scholar 

8. Goldstein, A.A: On steepest descent. SIAM J. Control 3, 147–151 (1965)

   MathSciNet  MATH  Google Scholar 

9. Ishikawa, S: Fixed points by a new iteration method. Proc. Am. Math. Soc. 44, 147–150 (1974)

   Article  MathSciNet  Google Scholar 

10. Khan, S.H.: A Picard-Mann hybrid iterative process. Fixed Point Theory Appl. 2013, 69. Springer Open Journal (2013)

11. Lemaréchal, C: A view of line search. In: Auslander, A., Oetti, W., Stoer, J. (eds.) , Optimization and Optimal Control, pp 59–78. Springer, Berlin (1981)

12. Luenberg, D.G., Ye, Y.: Linear and nonlinear programming. Springer Science+Business Media LLC, New York (2008)

    Google Scholar 

13. Mann, W.R.: Mean value methods in iterations. Proc. Am. Math. Soc. 4, 506–510 (1953)

    Article  MathSciNet  Google Scholar 

14. Molina, B., Raydan, M.: Preconditioned Barzilai–Borwein method for the numerical solution of partial differential equations. Numer. Algor. 13, 45–60 (1996)

    Article  MathSciNet  Google Scholar 

15. Moré, J.J., Thuente, D.J.: On line search algorithm with guaranteed sufficient decrease, Mathematics and Computer Science Division Preprint MCS-P153-0590. Argone National Laboratory, Argone (1990)

    Google Scholar 

16. Nesterov, Ye.E.: A method for solving the convex programming problem with convergence rate O\((\frac {1}{k^2})\). Dokl. Acad. Nauk SSSR 269(3), 543–547 (1983)

    Google Scholar 

17. Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equation in several variables. Academic Press, New York (1970)

    MATH  Google Scholar 

18. Petrović M.J.: An accelerated double step size method in unconstrained optimization. Appl. Math. Comput. 250, 309–319 (2015)

    MathSciNet  MATH  Google Scholar 

19. Petrović, M.J., Stanimirović, P.S.: Accelerated double direction method for solving unconstrained optimization problems. Math. Probl. Eng. 2014, Article ID 965104, 8 pp (2014)

20. Stanimirović, P.S., Milovanović, G.V., Petrović, M.J.: A transformation of accelerated double step size method for unconstrained optimization. Math. Probl. Eng. 2015, Article ID 283679, 8 pp (2015)

21. Potra, F.A., Shi, Y: Efficient line search algorithm for unconstrained optimization. J. Optim. Theory Appl. 85, 677–704 (1995)

    Article  MathSciNet  Google Scholar 

22. Powell, M.J.D.: Some global convergence properties of a variable-metric algorithm for minimization without exact line search. AIAM-AMS Proc. Phila. 9, 53–72 (1976)

    Google Scholar 

23. Picard, E: Memoire sur la theorie des equations aux derivees partielles et la methode des approximations successives. J. Math. Pures Appl. 6, 145–210 (1890)

    MATH  Google Scholar 

24. Rockafellar, R.T.: Convex analysis. Princeton University Press, Princeton (1970)

    Book  Google Scholar 

25. Shi, Z.-J.: Convergence of line search methods for unconstrained optimization. Appl. Math. Comput. 157, 393–405 (2004)

    MathSciNet  MATH  Google Scholar 

26. Stanimirović, P.S., Miladinović, M.B.: Accelerated gradient descent methods with line search. Numer. Algor. 54, 503–520 (2010)

    Article  MathSciNet  Google Scholar 

27. Sun, W., Yuan, Y.-X.: Optimization theory and methods: nonlinear programming. Springer, Berlin (2006)

    MATH  Google Scholar 

28. Wolfe, P: Convergence conditions for ascent methods. SIAM Rev. 11, 226–235 (1968)

    Article  MathSciNet  Google Scholar 

29. Zalinescu, C.: Convex analysis in general vector spaces. World Scientific, Singapore (2002)

    Book  Google Scholar 

Download references