[1]
|
A. B. Abubakar, A. H. Ibrahim, A. B. Muhammad and C. Tammer, A modified descent Dai-Yuan conjugate gradient method for constraint nonlinear monotone operator equations, Appl. Anal. Optim., 4 (2020), 1-24.
|
[2]
|
A. B. Abubakar and P. Kumam, A descent Dai-Liao conjugate gradient method for nonlinear equations, Numerical Algorithms, 81 (2019), 197-210.
doi: 10.1007/s11075-018-0541-z.
|
[3]
|
A. B. Abubakar and P. Kumam, An improved three-term derivative-free method for solving nonlinear equations, Comput. Appl. Math., 37 (2018), 6760-6773.
doi: 10.1007/s40314-018-0712-5.
|
[4]
|
A. B. Abubakar, P. Kumam and A. H. Ibrahim, Inertial Derivative-Free Projection Method for Nonlinear Monotone Operator Equations with Convex Constraints, IEEE Access. 2021.
|
[5]
|
J. Abubakar, P. Kumam, A. H. Ibrahim and et al., Inertial iterative schemes with variable step sizes for variational inequality problem involving pseudomonotone operator, Mathematics, 8 (2020), 609.
|
[6]
|
A. B. Abubakar, P. Kumam, A. H. Ibrahim, P. Chaipunya and S. A. Rano, New Hybrid Three-Term Spectral-Conjugate Gradient Method for Finding Solutions of Nonlinear Monotone Operator Equations with Applications, Mathematics and Computers in Simulation, 2021.
|
[7]
|
A. B. Abubakar, P. Kumam, A. H. Ibrahim and J. Rilwan, Derivative-free HS-DY-type method for solving nonlinear equations and image restoration, Heliyon, 6 (2020), e05400.
|
[8]
|
A. B. Abubakar, P. Kumam and H. Mohammad, A note on the spectral gradient projection method for nonlinear monotone equations with applications, Comput. Appl. Math., 39 (2020), Paper No. 129, 35 pp.
doi: 10.1007/s40314-020-01151-5.
|
[9]
|
A. B. Abubakar, P. Kumam, H. Mohammad and A. H. Ibrahim, PRP-like algorithm for monotone operator equations, Jpn. J. Ind. Appl. Math., 38 (2021), 805-822.
doi: 10.1007/s13160-021-00462-2.
|
[10]
|
A. B. Abubakar, K. Muangchoo, A. H. Ibrahim, J. Abubakar and S. A. Rano, FR-type algorithm for finding approximate solutions to nonlinear monotone operator equations, Arab. J. Math. (Springer), 10 (2021), 261-270.
doi: 10.1007/s40065-021-00313-5.
|
[11]
|
A. B. Abubakar, K. Muangchoo, A. H. Ibrahim, S. E. Fadugba, K. O. Aremu and L. O. Jolaoso, A modified scaled spectral-conjugate gradient-based algorithm for solving monotone operator equations, J. Math., 2021 (2021), Art. ID 5549878, 9 pp.
doi: 10.1155/2021/5549878.
|
[12]
|
A. B. Abubakar, K. Muangchoo, A. H. Ibrahim, A. B. Muhammad, L. O. Jolaoso and K. O. Aremu, A new three-term Hestenes-Stiefel type method for nonlinear monotone operator equations and image restoration, IEEE Access, 9 (2021), 18262-18277.
|
[13]
|
A. B. Abubakar, J. Rilwan, S. E. Yimer, A. H. Ibrahim and and I. Ahmed, Spectral three-term conjugate descent method for solving nonlinear monotone equations with convex constraints, Thai J. Math., 18 (2020), 501-517.
|
[14]
|
J. Abubakar, P. Kumam, A. H. Ibrahim and A. Padcharoen, Relaxed inertial Tseng's type method for solving the inclusion problem with application to image restoration, Mathematics, 8 (2020), 818.
|
[15]
|
J. Abubakar, K. Sombut, H. ur Rehman, A. H. Ibrahim and et al., An accelerated subgradient extragradient algorithm for strongly pseudomonotone variational inequality problems, Thai J. Math., 18 (2020), 166-187.
|
[16]
|
W. Aj and B. Wollenberg, Power Generation, Operation and Control, New York: John Wiley & Sons. 1996,592.
|
[17]
|
F. Alvarez and H. Attouch, An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Analysis, 9 (2001), 3-11.
doi: 10.1023/A:1011253113155.
|
[18]
|
H. Attouch, J. Peypouquet and P. Redont, A dynamical approach to an inertial forward-backward algorithm for convex minimization, SIAM J. Optim., 24 (2014), 232-256.
doi: 10.1137/130910294.
|
[19]
|
A. Auslender, M. Teboulle and S. Ben-Tiba, A logarithmic-quadratic proximal method for variational inequalities, Comput. Optim. Appl., 12 (1999), 31-40.
doi: 10.1023/A:1008607511915.
|
[20]
|
A. B. Abubakar, P. Kumam, M. Malik, P. Chaipunya and A. H. Ibrahim, A hybrid FR-DY conjugate gradient algorithm for unconstrained optimization with application in portfolio selection, AIMS Math., 6 (2021), 6506-6527.
doi: 10.3934/math.2021383.
|
[21]
|
A. B. Abubakar, P. Kumam, M. Malik and A. H. Ibrahim, A Hybrid Conjugate Gradient Based Approach for Solving Unconstrained Optimization and Motion Control Problems., Mathematics and Computers in Simulation, 2021.
|
[22]
|
R. I. Boţ and E. R. Csetnek, An inertial forward-backward-forward primal-dual splitting algorithm for solving monotone inclusion problems, Numer. Algorithms, 71 (2016), 519-540.
doi: 10.1007/s11075-015-0007-5.
|
[23]
|
R. I. Boţ and E. R. Csetnek, A hybrid proximal-extragradient algorithm with inertial effects, Numer. Funct. Anal. Optim., 36 (2015), 951-963.
doi: 10.1080/01630563.2015.1042113.
|
[24]
|
R. I. Boţ, E. R. Csetnek and C. Hendrich, Inertial Douglas–Rachford splitting for monotone inclusion problems, Appl. Math. Comput., 256 (2015), 472-487.
doi: 10.1016/j.amc.2015.01.017.
|
[25]
|
C. Chen, R. H. Chan, S. Ma and J. Yang, Inertial proximal ADMM for linearly constrained separable convex optimization, SIAM J. Imaging Sci., 8 (2015), 2239-2267.
doi: 10.1137/15100463X.
|
[26]
|
P. Chuasuk, F. Ogbuisi, Y. Shehu and P. Cholamjiak, New inertial method for generalized split variational inclusion problems, Journal of Industrial & Management Optimization, (2020).
|
[27]
|
J. E. Dennis Jr. and J. J. Moré, A characterization of superlinear convergence and its application to quasi-Newton methods, Math. Comp., 28 (1974), 549-560.
doi: 10.1090/S0025-5718-1974-0343581-1.
|
[28]
|
J. E. Dennis Jr. and J. J. Moré, Quasi-Newton methods, motivation and theory, SIAM Rev., 19 (1977), 46-89.
doi: 10.1137/1019005.
|
[29]
|
J. E. Dennis Jr. and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM; 1996.
doi: 10.1137/1.9781611971200.
|
[30]
|
S. P. Dirkse and M. C. Ferris, MCPLIB: A collection of nonlinear mixed complementarity problems, Optimization Methods and Software, 5 (1995), 319-345.
|
[31]
|
E. D. Dolan and J. J. Moré, Benchmarking optimization software with performance profiles, Math. Program., 91 (2002), 201-213.
doi: 10.1007/s101070100263.
|
[32]
|
Q. L. Dong, Y. J. Cho, L. L. Zhong and Th. M. Rassias, Inertial projection and contraction algorithms for variational inequalities, J. Global Optim., 70 (2018), 687-704.
doi: 10.1007/s10898-017-0506-0.
|
[33]
|
M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer Science & Business Media; 2010.
doi: 10.1007/978-1-4419-7011-4.
|
[34]
|
M. A. Figueiredo, R. D. Nowak and S. J. Wright, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems, IEEE Journal of Selected Topics in Signal Processing, 1 (2007), 586-597.
|
[35]
|
P. Gao and C. He, An efficient three-term conjugate gradient method for nonlinear monotone equations with convex constraints, Calcolo, 55 (2018), Paper No. 53, 17 pp.
doi: 10.1007/s10092-018-0291-2.
|
[36]
|
A. H. Ibrahim, J. Deepho, A. B. Abubakar and A. Adamu, A three-term Polak-Ribiére-Polyak derivative-free method and its application to image restoration, Scientific African, 13 (2021), e00880. Available from: https://www.sciencedirect.com/science/article/pii/S2468227621001848.
|
[37]
|
A. H. Ibrahim, J. Deepho, A. B. Abubakar and K. O. Aremu, A Modified Liu-Storey-Conjugate Descent Hybrid Projection Method for Convex Constrained Nonlinear Equations and Image Restoration, Numerical Algebra, Control & Optimization, 2021.
|
[38]
|
A. H. Ibrahim, G. A. Isa, H. Usman, J. Abubakar and A. B. Abubakar, Derivative-free RMIL conjugate gradient method for convex constrained equations, Thai J. Math., 18 (2019), 212-232.
|
[39]
|
A. H. Ibrahim and P. Kumam, Re-modified derivative-free iterative method for nonlinear monotone equations with convex constraints, Ain Shams Engineering Journal, (2021).
|
[40]
|
A. H. Ibrahim, P. Kumam, A. B. Abubakar, J. Abubakar and A. B. Muhammad, Least-square-based three-term conjugate gradient projection method for $\ell_1$-norm problems with application to compressed sensing, Mathematics, 8 (2020), 602.
|
[41]
|
A. H. Ibrahim, P. Kumam, A. B. Abubakar, U. Batsari Yusuf, S. E. Yimer and K. O. Aremu, An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration, AIMS Math., 6 (2021), 235-260.
doi: 10.3934/math.2021016.
|
[42]
|
A. H. Ibrahim, P. Kumam, A. B. Abubakar, W. Jirakitpuwapat and J. Abubakar, A hybrid conjugate gradient algorithm for constrained monotone equations with application in compressive sensing, Heliyon, 6 (2020), e03466.
|
[43]
|
A. H. Ibrahim, P. Kumam, A. B. Abubakar, U. B. Yusuf and J. Rilwan, Derivative-free conjugate residual algorithms for convex constraints nonlinear monotone equations and signal recovery, J. Nonlinear Convex Anal., 21 (2020), 1959-1972.
|
[44]
|
A. H. Ibrahim, P. Kumam, B. A. Hassan, A. B. Abubakar and J. Abubakar, A derivative-free three-term hestenes-stiefel type method for constrained nonlinear equations and image restoration, International Journal of Computer Mathematics, 0 (2021), 1-22.
doi: 10.1080/00207160.2021.1946043.
|
[45]
|
A. H. Ibrahim, P. Kumam and W. Kumam, A family of derivative-free conjugate gradient methods for constrained nonlinear equations and image restoration, IEEE Access, 8 (2020), 162714-162729.
|
[46]
|
A. H. Ibrahim, K. Muangchoo, A. B. Abubakar, A. D. Adedokun and H. Mohammed, Spectral conjugate gradient like method for signal reconstruction, Thai J. Math., 18 (2020), 2013-2022.
|
[47]
|
A. H. Ibrahim, K. Muangchoob, N. S. Mohamedc and A. B. Abubakar, Derivative-free SMR conjugate gradient method for con-straint nonlinear equations, Journal of Mathematics and Computer Science, 24 (2022), 147-164.
|
[48]
|
W. La Cruz, J. M. Martínez and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems: Theory and experiments, Citeseer, 2004; Technical Report RT-04-08 (https://www.ime.unicamp.br/ martinez/lmrreport.pdf).
|
[49]
|
Q. Li and D.-H. Li, A class of derivative-free methods for large-scale nonlinear monotone equations, IMA J. Numer. Anal., 31 (2011), 1625-1635.
doi: 10.1093/imanum/drq015.
|
[50]
|
D. A. Lorenz and T. Pock, An inertial forward-backward algorithm for monotone inclusions, J. Math. Imaging Vision, 51 (2015), 311-325.
doi: 10.1007/s10851-014-0523-2.
|
[51]
|
K. Meintjes and A. P. Morgan, A methodology for solving chemical equilibrium systems, Appl. Math. Comput., 22 (1987), 333-361.
doi: 10.1016/0096-3003(87)90076-2.
|
[52]
|
H. Mohammad, Barzilai-Borwein-like method for solving large-scale non-linear systems of equations, J. Nigerian Math. Soc., 36 (2017), 71-83.
|
[53]
|
H. Mohammad and A. B. Abubakar, A descent derivative-free algorithm for nonlinear monotone equations with convex constraints, RAIRO Oper. Res., 54 (2020), 489-505.
doi: 10.1051/ro/2020008.
|
[54]
|
B. T. Polyak, Some methods of speeding up the convergence of iteration methods, Ž. Vyčisl. Mat i Mat. Fiz., 4 (1964), 791–803.
|
[55]
|
L. Qi and J. Sun, A nonsmooth version of Newton's method, Math. Programming, 58 (1993), 353-367.
doi: 10.1007/BF01581275.
|
[56]
|
M. V. Solodov and B. F. Svaiter, A new projection method for variational inequality problems, SIAM J. Control Optim., 37 (1999), 765-776.
doi: 10.1137/S0363012997317475.
|
[57]
|
M. Sun, J. Liu and Y. Wang, Two improved conjugate gradient methods with application in compressive sensing and motion control, Math. Probl. Eng., 2020 (2020), Art. ID 9175496, 11 pp.
doi: 10.1155/2020/9175496.
|
[58]
|
D. V. Thong and D. V. Hieu, An inertial method for solving split common fixed point problems, J. Fixed Point Theory Appl., 19 (2017), 3029-3051.
doi: 10.1007/s11784-017-0464-7.
|
[59]
|
D. V. Thong and D. V. Hieu, Modified subgradient extragradient method for variational inequality problems, Numer. Algorithms, 79 (2018), 597-610.
doi: 10.1007/s11075-017-0452-4.
|
[60]
|
Y. Xiao and H. Zhu, A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing, J. Math. Anal. Appl., 405 (2013), 310-319.
doi: 10.1016/j.jmaa.2013.04.017.
|
[61]
|
N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method, In: Topics in Numerical Analysis, 15, Springer, Vienna, (2001), 239–249.
doi: 10.1007/978-3-7091-6217-0_18.
|
[62]
|
Z. Yu, J. Lin, J. Sun, Y. Xiao, L. Liu and Z. Li, Spectral gradient projection method for monotone nonlinear equations with convex constraints, Appl. Numer. Math., 59 (2009), 2416-2423.
doi: 10.1016/j.apnum.2009.04.004.
|