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Journal of Applied Mathematics and Computing
Erschienen in: Journal of Applied Mathematics and Computing 1/2024

13.12.2023 | Original Research

A new hybrid CGPM-based algorithm for constrained nonlinear monotone equations with applications

verfasst von: Guodong Ma, Liqi Liu, Jinbao Jian, Xihong Yan

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1/2024

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Abstract

The conjugate gradient projection method (CGPM) has good theoretical properties and numerical performance for solving large-scale nonlinear monotone equations with convex constraints. In this paper, by designing a modified adaptive line search, a new hybrid CGPM-based algorithm is proposed. The search direction satisfies the sufficient descent and trust region properties which are independent of the choices of the line search. The global convergence of the algorithm is analyzed without the Lipschitz continuity. The linear convergence rate is established under some appropriate assumptions. Some preliminary numerical experiment results are reported, which show that our proposed algorithm is promising. Finally, the proposed algorithm is extended to solve the sparse signal and image restoration problems in compressed sensing.
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Literatur
1.
Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)
2.
Meintjes, K., Morgan, A.P.: A methodology for solving chemical equilibrium systems. Appl. Math. Comput. 22(4), 333–361 (1987)MathSciNet
3.
Dai, Z.F., Zhou, H.T., Wen, F.H., He, S.Y.: Efficient predictability of stock return volatility: the role of stock market implied volatility. N. Am. J. Econ. Financ. 52, 101174 (2020)CrossRef
4.
Barari, M., Karimi, H.R., Razaghian, F.: Analog circuit design optimization based on evolutionary algorithms. Math. Probl. Eng. 2014, 593684 (2014)CrossRef
5.
Solodov, M.V., Svaiter, B.F.: A globally convergent inexact Newton method for systems of monotone equations. In: Fukushima, M., Qi, L.Q. (eds.) Reformulation: Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods, pp. 355–369. Springer, Boston, MA (1999)
6.
Sun, D.F., Womersley, R., Qi, H.D.: A feasible semismooth asymptotically Newton method for mixed complementarity problems. Math. Program. 94(1), 167–187 (2002)MathSciNetCrossRef
7.
Yuan, G.L., Lu, X.W., Wei, Z.X.: BFGS trust-region method for symmetric nonlinear equations. J. Comput. Appl. Math. 230(1), 44–58 (2009)ADSMathSciNetCrossRef
8.
Yuan, G.L., Wei, Z.X., Lu, X.W.: A BFGS trust-region method for nonlinear equations. Computing 92(4), 317–333 (2011)MathSciNetCrossRef
9.
Luo, Y.Z., Tang, G.J., Zhou, L.N.: Hybrid approach for solving systems of nonlinear equations using chaos optimization and quasi-Newton method. Appl. Soft Comput. 8(2), 1068–1073 (2008)CrossRef
10.
Buhmiler, S., Krejič, N., Lužanin, Z.: Practical quasi-Newton algorithms for singular nonlinear systems. Numer. Algorithms. 55(4), 481–502 (2010)MathSciNetCrossRef
11.
Solodov, M.V., Svaiter, B.F.: A new projection method for variational inequality problems. SIAM J. Control. Optim. 37(3), 765–776 (1999)MathSciNetCrossRef
12.
Ou, Y.G., Li, J.Y.: A new derivative-free SCG-type projection method for nonlinear monotone equations with convex constraints. J. Appl. Math. Comput. 56, 195–216 (2018)MathSciNetCrossRef
13.
Zhou, W.J., Wang, F.: A PRP-based residual method for large-scale monotone nonlinear equations. Appl. Math. Comput. 261, 1–7 (2015)MathSciNet
14.
Zheng, L., Yang, L., Liang, Y.: A conjugate gradient projection method for solving equations with convex constraints. J. Comput. Appl. Math. 375, 112781 (2020)MathSciNetCrossRef
15.
Sun, M., Liu, J.: New hybrid conjugate gradient projection method for the convex constrained equations. Calcolo 53(3), 399–411 (2016)MathSciNetCrossRef
16.
Xiao, Y.H., Zhu, H.: A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing. J. Math. Anal. Appl. 405(1), 310–319 (2013)MathSciNetCrossRef
17.
Ibrahim, A.H., Kumam, P., Abubakar, A.B., Adamu, A.: Accelerated derivative-free method for nonlinear monotone equations with an application. Numer. Linear. Algebr. 29(3), e2424 (2022)MathSciNetCrossRef
18.
Abubakar, A.B., Kumam, P., Ibrahim, A.H., Chaipunya, P., Rano, S.A.: New hybrid three-term spectral-conjugate gradient method for finding solutions of nonlinear monotone operator equations with applications. Math. Comput. Simulat. 201, 670–683 (2022)MathSciNetCrossRef
19.
Abubakar, A.B., Kumam, P., Mohammad, A.H., Ibrahim, A.H., Kiri, A.I.: A hybrid approach for finding approximate solutions to constrained nonlinear monotone operator equations with applications. Appl. Numer. Math. 177, 79–92 (2022)MathSciNetCrossRef
20.
Wu, X.Y., Shao, H., Liu, P.J., Zhuo, Y.: An inertial spectral CG projeciton method based on the memoryless BFGS update. J. Optimiz. Theory. App. 198, 1130–1155 (2023)CrossRef
21.
22.
Liu, J.K., Sun, Y., Zhao, Y.X.: A derivative-free projection algorithm for solving pseudo monotone equations with convex constraints (in Chinese). Math. Numer. Sin. 43(03), 388–400 (2021)MathSciNet
23.
Zhang, N., Liu, J.K.: A self-adaptive projection method for nonlinear monotone equations with convex constraints. J. Ind. Manag. Optim. 19(11), 8152–8163 (2023)MathSciNetCrossRef
24.
Liu, P.J., Shao, H., Wang, Y., Wu, X.Y.: A three-term CGPM-based algorithm without Lipschitz continuity for constrained nonlinear monotone equations with applications. Appl. Numer. Math. 175, 98–107 (2022)MathSciNetCrossRef
25.
Ma, G.D., Lin, H., Jin, W.H., Han, D.L.: Two modified conjugate gradient methods for unconstrained optimization with applications in image restoration problems. J. Appl. Math. Comput. 68, 4733–4758 (2022)MathSciNetCrossRef
26.
Abubakar, A.B., Kumam, P., Malik, M., Ibrahim, A.H.: A hybrid conjugate gradient based approach for solving unconstrained optimization and motion control problems. Math. Comput. Simulat. 201, 640–657 (2022)MathSciNetCrossRef
27.
Liu, Y.F., Zhu, Z.B., Zhang, B.X.: Two sufficient descent three-term conjugate gradient methods for unconstrained optimization problems with applications in compressive sensing. J. Appl. Math. Comput. 68, 1787–1816 (2022)MathSciNetCrossRef
28.
Narushima, Y., Yabe, H., Ford, J.A.: three-term conjugate gradient method with sufficient descent property for unconstrained optimization. SIAM J. Optimiz. 21(1), 212–230 (2011)MathSciNetCrossRef
29.
Jiang, X.Z., Yang, H.H., Yin, J.H., Liao, W.: A three-term conjugate gradient algorithm with restart procedure to solve image restoration problems. J. Comput. Appl. Math. 424, 115020 (2023)MathSciNetCrossRef
30.
Zhang, L., Zhou, W.J.: Spectral gradient projection method for solving nonlinear monotone equations. J. Comput. Appl. Math. 196(2), 478–484 (2006)ADSMathSciNetCrossRef
31.
Zhou, W.J., Li, D.H.: A globally convergent BFGS method for nonlinear monotone equations without any merit functions. Math. Comput. 77(264), 2231–2240 (2008)ADSMathSciNetCrossRef
32.
Amini, K., Kamandi, A.: A new line search strategy for finding separating hyperplane in projection-based methods. Numer. Algorithms 70(3), 559–570 (2015)MathSciNetCrossRef
33.
Yin, J.H., Jian, J.B., Jiang, X.Z., Liu, M.X., Wang, L.Z.: A hybrid three-term conjugate gradient projection method for constrained nonlinear monotone equations with applications. Numer. Algorithms 88, 389–418 (2021)MathSciNetCrossRef
34.
Zarantonello, E.H.: Projections on Convex Sets in Hilbert Space and Spectral Theory. Academic Press, New York (1971)
35.
Ibrahim, A.H., Kumam, P., Sun, M., Chaipunya, P., Abubakar, A.B.: Projection method with inertial step for nonlinear equations: application to Signal Recovery. J. Ind. Manag. Optim. 19(1), 30–55 (2023)MathSciNetCrossRef
36.
Ma, G.D., Jin, J.C., Jian, J.B., Yin, J.H., Han, D.L.: A modified inertial three-term conjugate gradient projection method for constrained nonlinear equations with applications in compressed sensing. Numer. Algorithms 92(3), 1621–1653 (2023)MathSciNetCrossRef
37.
Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Math. Program. 91(2), 201–213 (2002)MathSciNetCrossRef
38.
Banham, M.R., Katsaggelos, A.K.: Digital image restoration. IEEE Signal. Proc. Mag. 14(2), 24–41 (1997)CrossRef
39.
Chan, C.L., Katsaggelos, A.K., Sahakian, A.V.: Image sequence filtering in quantum-limited noise with applications to low-dose fluoroscopy. IEEE T. Med. Imaging 12(3), 610–621 (1993)CrossRef
40.
Figueiredo, M.A., Nowak, R.D., Wright, S.J.: Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems. IEEE J-STSP. 1(4), 586–597 (2007)
41.
Xiao, Y.H., Wang, Q.Y., Hu, Q.J.: Non-smooth equations based method for \(\ell _{1}\)-norm problems with applications to compressed sensing. Nonlinear. Anal-Theor. 74(11), 3570–3577 (2011)MathSciNetCrossRef
Metadaten
Titel
A new hybrid CGPM-based algorithm for constrained nonlinear monotone equations with applications
verfasst von
Guodong Ma
Liqi Liu
Jinbao Jian
Xihong Yan
Publikationsdatum
13.12.2023
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1/2024
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-023-01960-x

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