Open Access
Issue |
RAIRO-Oper. Res.
Volume 57, Number 5, September-October 2023
|
|
---|---|---|
Page(s) | 2561 - 2584 | |
DOI | https://doi.org/10.1051/ro/2023099 | |
Published online | 10 October 2023 |
- M. Abdullahi, A.S. Halilu, A.M. Awwal and N. Pakkaranang, On efficient matrix-free method via quasi-newton approach for solving system of nonlinear equations. Adv. Theory Nonlinear Anal. App. 5 (2021) 568–579. [Google Scholar]
- A.B. Abubakar, P. Kumam, A.M. Awwal and P. Thounthong, A modified self-adaptive conjugate gradient method for solving convex constrained monotone nonlinear equations for signal reovery problems. Mathematics 7 (2019) 693. [CrossRef] [Google Scholar]
- A.B. Abubakar, P. Kumam, H. Mohammad, A.M. Awwal and S. Kanokwan, A modified Fletcher-Reeves conjugate gradient method for monotone nonlinear equations with some applications. Mathematics 7 (2019) 745. [CrossRef] [Google Scholar]
- A.B. Abubakar, P. Kumam and A.M. Awwal, Global convergence via descent modified three-term conjugate gradient projection algorithm with applications to signal recovery. Results Appl. Math. 4 (2019) 100069. [CrossRef] [Google Scholar]
- 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. [CrossRef] [PubMed] [Google Scholar]
- A.B. Abubakar, P. Kumam, H. Mohammad and A.M. Awwal, A Barzilai-Borwein gradient projection method for sparse signal and blurred image restoration. J. Franklin Inst. 357 (2020) 7266–7285. [CrossRef] [MathSciNet] [Google Scholar]
- A.B. Abubakar, Y. Feng and A.H. Ibrahim, Inertial projection method for solving monotone operator equations, in 2022 12th International Conference on Information Science and Technology (ICIST). IEEE (2022) 1–7. [Google Scholar]
- A.B. Abubakar, P. Kumam, H. Mohammad, A.H. Ibrahim and A.I. Kiri, A hybrid approach for finding approximate solutions to constrained nonlinear monotone operator equations with applications. Appl. Numer. Math. 177 (2022) 79–92. [CrossRef] [MathSciNet] [Google Scholar]
- A.M. Awwal, P. Kumam and A.B. Abubakar, A modified conjugate gradient method for monotone nonlinear equations with convex constraints. Appl. Numer. Math. 145 (2019) 507–520. [CrossRef] [MathSciNet] [Google Scholar]
- S. Babaie-Kafaki and N. Mahdavi-Amiri, Two modified hybrid conjugate gradient methods based on a hybrid secant equation. Math. Modell. Anal. 18 (2013) 32–52. [CrossRef] [Google Scholar]
- A. Beck and M. Teboulle, A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imag. Sci. 2 (2009) 183–202. [CrossRef] [Google Scholar]
- E.G. Birgin, J. Martínez and M. Raydan, Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Optim. 10 (2000) 1196–1211. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Dai and Y. Yuan, A nonlinear conjugate gradient method with a strong global convergence property. SIAM J. Optim. 10 (1999) 177–182. [CrossRef] [MathSciNet] [Google Scholar]
- J.E. Dennis and J.J. Moré, A characterization of superlinear convergence and its application to Quasi-Newton methods. Math. Comput. 28 (1974) 549–560. [CrossRef] [Google Scholar]
- J. Dennis, E. John and J.J. Moré, Quasi-Newton methods, motivation and theory. SIAM Rev. 19 (1977) 46–89. [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]
- M.A.T. Figueiredo and R.D. Nowak, An EM algorithm for wavelet-based image restoration. IEEE Trans. Image Process. 12 (2003) 906–916. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
- M.A.T. Figueiredo, R.D. Nowak and S.J. Wright, Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J. Sel. Top. Signal Process. 1 (2007) 586–597. [CrossRef] [Google Scholar]
- R. Fletcher, An overview of unconstrained optimization, in Algorithms for Continuous Optimization. NATO ASI Series. Vol. 434. Springer, Dordrecht (1994) 109–143. [CrossRef] [Google Scholar]
- R. Fletcher and C.M. Reeves, Function minimization by conjugate gradients. Comput. J. 7 (1964) 149–154. [Google Scholar]
- A.S. Halilu, A. Majumder, M.Y. Waziri and H. Abdullahi, Double direction and step length method for solving system of nonlinear equations. Eur. J. Mol. Clin. Med. 7 (2020) 3899–3913. [Google Scholar]
- A.S. Halilu, M.Y. Waziri and Y.B. Musa, Inexact double step length method for solving systems of nonlinear equations. Stat. Optim. Inf. Comput. 8 (2020) 165–174. [CrossRef] [MathSciNet] [Google Scholar]
- A.S. Halilu, A. Majumder, M.Y. Waziri and K. Ahmed, Signal recovery with convex constrained nonlinear monotone equations through conjugate gradient hybrid approach. Math. Comput. Simul. 187 (2021) 520–539. [CrossRef] [Google Scholar]
- M.R. Hestsenes and E. Stiefel, Methods of conjugate gradients for solving linear equations. J. Res. Nat. Bur. Stand. 49 (1952) 409. [CrossRef] [Google Scholar]
- 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. Numer. Alg. Control Optim. (2021). DOI: 10.3934/naco.2021022. [Google Scholar]
- A.H. Ibrahim, J. Deepho, A.B. Abubakar and A. Kamandi, A globally convergent derivative-free projection algorithm for signal processing. J. Interdisciplinary Math. 25 (2022) 2301–2320. [CrossRef] [Google Scholar]
- A.H. Ibrahim, P. Kumam, A.B. Abubakar, M.S. Abdullahi and H. Mohammad, A dai-liao-type projection method for monotone nonlinear equations and signal processing. Demonstratio Math. 55 (2022) 978–1013. [CrossRef] [MathSciNet] [Google Scholar]
- A.H. Ibrahim, P. Kumam, A.B. Abubakar and J. Abubakar, A derivative-free projection method for nonlinear equations with non-lipschitz operator: application to lasso problem. Math. Methods Appl. Sci. 46 (2023) 9006–9027. [CrossRef] [MathSciNet] [Google Scholar]
- R.I. Kachurovskii, Monotone operators and convex functionals. Uspekhi Matematicheskikh Nauk 15 (1960) 213–215. [Google Scholar]
- P. Kumam, A.B. Abubakar, M. Malik, A.H. Ibrahim, N. Pakkaranang and B. Panyanak, A hybrid HS-LS conjugate gradient algorithm for unconstrained optimization with applications in motion control and image recovery. J. Comput. Appl. Math. 433 (2023) 115304. [CrossRef] [Google Scholar]
- W. La Cruz, J. Martínez and M. Raydan, Spectral residual method without gradient information for solving large-scale nonlinear systems of equations. Math. Comput. 75 (2006) 1429–1448. [CrossRef] [Google Scholar]
- D. Li and M. Fukushima, A globally and superlinearly convergent Gauss–Newton-based BFGS method for symmetric nonlinear equations. SIAM J. Numer. Anal. 37 (1999) 152–172. [CrossRef] [MathSciNet] [Google Scholar]
- J.K. Liu and S.J. Li, A projection method for convex constrained monotone nonlinear equations with applications. Comput. Math. App. 70 (2015) 2442–2453. [Google Scholar]
- Y. Liu and C. Storey, Efficient generalized conjugate gradient algorithms, part 1: theory. J. Optim. Theory App. 69 (1991) 129–137. [CrossRef] [Google Scholar]
- K. Meintjes and A.P. Morgan, A methodology for solving chemical equilibrium systems. Appl. Math. Comput. 22 (1987) 333–361. [Google Scholar]
- G.J. Minty, Monotone (nonlinear) operators in hilbert space. Duke Math. J. 29 (1962) 341–346. [CrossRef] [MathSciNet] [Google Scholar]
- G. Peiting, H. Chuanjiang and L. Yang, An adaptive family of projection methods for constrained monotone nonlinear equations with applications. Appl. Math. Comput. 359 (2019) 1–16. [CrossRef] [MathSciNet] [Google Scholar]
- E. Polak and G. Ribiere, Note sur la convergence de méethodes de directions conjuguées. ESAIM: Math. Model. Numer. Anal. – Modél. Math. Anal. Numér. 3 (1969) 35–43. [Google Scholar]
- M.V. Solodov and B.F. Svaiter, A globally convergent inexact Newton method for systems of monotone equations, in Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods. Springer (1998) 355–369. [CrossRef] [Google Scholar]
- E. Van Den Berg and M.P. Friedlander, Probing the pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31 (2008) 890–912. [Google Scholar]
- X.Y. Wang, S.J. Li and X.P. Kou, A self-adaptive three-term conjugate gradient method for monotone nonlinear equations with convex constraints. Calcolo 53 (2016) 133–145. [CrossRef] [MathSciNet] [Google Scholar]
- A.J. Wood and B.F. Wollenberg, Wollenberg, Power Generation, Operation and Control, John Wiley & Sons, New York (1996) 592. [Google Scholar]
- Y. Xiao, Q. Wang and Q. Hu, Non-smooth equations based method for ℓ1-norm problems with applications to compressed sensing. Nonlinear Anal. Theory Methods App. 74 (2011) 3570–3577. [CrossRef] [Google Scholar]
- 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. [CrossRef] [MathSciNet] [Google Scholar]
- G. Yuan and X. Lu, A new backtracking inexact BFGS method for symmetric nonlinear equations. Comput. Math. App. 55 (2008) 116–129. [Google Scholar]
- E.H. Zarantonello, Solving Functional Equations by Contractive Averaging. Mathematics Research Center, United States Army, University of Wisconsin (1960). [Google Scholar]
- L. Zheng, L. Yang and Y. Liang, A modified spectral gradient projection method for solving non-linear monotone equations with convex constraints and its application. IEEE Access 8 (2020) 92677–92686. [Google Scholar]
- D. Zhifeng, Z. Huan and K. Jie, New technical indicators and stock returns predictability. Int. Rev. Econ. Finance 71 (2021) 127–142. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.