Secant Condition Free of a Spectral PRP Conjugate Gradient Method

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    Recently conjugate gradient method have been in practice widely to solve unconstrained minimization problems as a result of fewer storage locations and less computational expensive in dealing with the large-scale problems. In this work, we suggested a spectral PRP CG method without employing the secant condition and use some unconstrained problems with many variables to prove its sufficient descent as well as global convergence, the results is validated by apply exact line search.

                                                                                                                                          

     


  • Keywords


    Global convergence; exact line search; spectral CG; secant condition; sufficient descent property.

  • References


      [1] M. Raydan (1997). The Barzilai and J.M. Borwein gradient methods for the large scale unconstrained minimization in extreme problems, SIAM. J. Optim., 7(1), 26-33.

      [2] E. Dolan, J.J. More (2002). Benchmarking optimization software with performance profile, Math. Prog., 91, 201-213.

      [3] E.G. Birgin and J.M. Martinez (2011). A spectral conjugate gradient method for unconstrained optimization, Appl. Math. Optim., 43(2), 117-128.

      [4] X. Wu (2015). A new spectral Polak- Ribière -Polak conjugate gradient method, ScienceAsia, 41, 345-349.

      [5] G. Zoutendijk (1970). Nonlinear programming, computational methods, in J Abadie (Ed.), Integer and Nonlinear Programming, Amsterdam: North-Holland, pp. 37-86.

      [6] J. C. Gilbert, J. Nocedal (1992). Global convergence properties of conjugate gradient methods for optimization, SIAM. J. Optim., 2, 21-42.

      [7] C. Hu, Z. Wan (2013). An extended spectral conjugate gradient method for unconstrained optimization problems, British Journal of Math. and Computer Science, 3, 86-98.

      [8] H. Huang, Z. Wei, Y. Shengwei (2007). The proof of the sufficient decent condition of the Wei-Yao-Liu conjugate gradient method under the strong Wolfe-Powell line search, Applied Mathematics and Computation., 189, 1241–1245.

      [9] M.J.D. Powell (1984). Non-convex minimization calculations and the conjugate gradient method. Lecture Notes in Mathematics, 1066, 122-241.

      [10] M.J.D. Powell (1977). Restart procedures for the conjugate gradient method, Math. Program., 12, 241-254.

      [11] J. Barzilai, J.M. Borwein (1988). Two point stepsize gradient methods, IMA J Numer Anal., 8, 141-148.

      [12] X. Du, J. Liu (2011). Global convergence of a spectral HS conjugate gradient method, Procedia Engineering, 15, 1487-1492.

      [13] N. Zull, M. Rivaie, M. Mamat, Z Salleh, Z. Amani (2015). Global convergence of a Spectral conjugate gradient by using strong Wolfe line search, Appl. Math. Sci., 63, 3105-3117.

      [14] W.W. Hager, H. Zhang (2006). A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization, 2(1), 35-58.

      [15] N. Andrei (2008). An unconstrained optimization test functions collection, Adv. Modell. Optim., 10, 147-161.

      [16] A. Y. Usman, M. Mamat, M. Rivaie, A. M. Mohamad and B. Y. Rabi’u (2018). Secant free condition of a spectral WYL and its global convergence properties. Far East Journal of Mathematical Science, 103(12), 1889-1902.

      [17] A. Y. Usman, M. Mamat, M. Rivaie, A. M. Mohamad and J. Sabi’u (2018). A recent modification on Dai-Liao conjugate gradient method for solving symmetric nonlinear equations. Far East Journal of Mathematical Science, 103(12), 1961-1974.

      [18] N. Z. Abidin, M. Mamat, B. Dangerfield, J. H. Zulkepli, M. A. Baten and A. Wibowo (2014). Combating obesity through healthy eating behavior: A call for system dynamics optimization. Plos One, 9(12), 1-17.

      [19] M. Mamat, Y. Rokhayati, N. M. M. Noor and I. Mohd (2011). Optimizing human diet problem with puzzy price using fuzzy linear programming approach. Pakistan Journal of Nutrition, 10(6), 594-598.

      [20] A. Abashar, M. Mamat, M. Rivaie and I. Mohd (2014). Global convergence properties of a new class of conjugate gradient method for unconstrained optimization. Applied Mathematical Sciences Issue, 65-68, 3307-3319.

      [21] A. Abashar, M. Mamat, M. Rivaie, I. Mohd and O. Omer (2014). The proof of sufficient descent condition for a new type of conjugate gradient methods. AIP Conference Proceedings, 1602, 296-303.


 

View

Download

Article ID: 23470
 
DOI: 10.14419/ijet.v7i3.28.23470




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.