A Class of Derivative-Free CG Projection Methods for Nonsmooth Equations with an Application to the LASSO Problem
Tóm tắt
Từ khóa
Tài liệu tham khảo
Wood, A.J., Wollenberg, B.F.: Power Generation, Operation, and Control. Wiley, New York (1996)
Meintjes, K., Morgan, A.P.: A methodology for solving chemical equilibrium systems. Appl. Math. Comput. 22, 333–361 (1987)
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, 310–319 (2013)
Sun, M., Liu, J.: The convergence rate of the proximal alternating direction method of multipliers with indefinite proximal regularization. J. Inequ. Appl. 2017, 19 (2017)
Zhou, B., Duam, G.R., Lin, Z.: A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. Automatica 47, 316–325 (2011)
La Cruz, W., Raydan, M.: Nonmonotone spectral methods for large-scale nonlinear systems. Optim. Methods Softw. 18, 583–599 (2003)
La Cruz W., Mart$$\grave{\rm i}$$nez J.M., Raydan M.: Spectral residual method without gradient information for solving large- scale nonlinear systems of equations. Math. Comput. 75, 429–1448 (2006)
Zhang, L., Zhou, W.J.: Spectral gradient projection method for solving nonlinear monotone equations. J. Comput. Appl. Math. 196, 478–484 (2006)
Barzilai, J., Borwein, J.M.: Two-point step size gradient methods. IMA J. Numer. Anal. 1988(8), 141–148 (1988)
Solodov, M.V., Svaiter, B.F.: A globally convergent inexact Newton method for system of monotone equations. In: Fukushima, M., Qi, L. (eds.) Reformulation: Nonsmooth, Piecewise Smooth, Semi- smooth and Smoothing Methods, pp. 355–369. Kluwer Academic Publishers, Dordrecht (1999)
Yu, Z.S., Lin, J., Sun, J., Xiao, Y.H., Liu, L.Y., Li, Z.H.: Spectral gradient projectionmethod formonotone nonlinear equations with convex constraints. Appl. Numer. Math. 59, 2416–2423 (2009)
Yu, G.H., Niu, S.Z., Ma, J.H.: Multivariate spectral gradient projectionmethod for nonlinear monotone equations with convex constraints. J. Ind. Manag. Optim. 9, 117–129 (2013)
Liu, J., Duan, Y.R.: Two spectral gradient projection methods for constrained equations and their linear convergence rate. J. Inequ. Appl. 2015, 8 (2015)
Cheng, W.Y.: A PRP type method for systems of monotone equations. Math. Comput. Model. 50, 15–20 (2009)
Li, Q.N., Li, D.H.: A class of derivative-free methods for large-scale nonlinear monotone equations. IMA J. Numer. Anal. 31, 1625–1635 (2011)
Li, D.H., Wang, X.L.: A modified Fletcher–Reeves-type derivative-free method for symmetric nonlinear equations. Numer. Algebra Control Optim. 1(1), 71–82 (2012)
Sun, X.L.: A two-term Fletcher–Reeves conjugate gradient method for monotone constrained equations and its application in compressive sensing. ICIC Express Lett. 9(11), 2987–2992 (2015)
Sun, M., Liu, J.: A modified Hestenes-Stiefel projection method for constrained nonlinear equations and its linear convergence rate. J. Appl. Math. Comput. 49(1–2), 145–156 (2015)
Sun, M., Liu, J.: New hybrid conjugate gradient projection method for the convex constrained equations. Calcolo 53, 399–411 (2016)
Yuan, G.L., Zhang, M.J.: A three-terms Polak-Ribi$$\grave{\rm e}$$re–Polyak conjugate gradient algorithm for large-scale nonlinear equations. J. Comput. Appl. Math. 286, 186–195 (2015)
Dai, Z.F., Chen, X.H., Wen, F.H.: A modified Perry’s conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations. Appl. Math. Comput. 270(1), 378–386 (2015)
Liu, J.K., Li, S.J.: Multivariate spectral DY-type projection method for convex constrained nonlinear monotone equations. J. Ind. Manag. Optim. 13(1), 283–295 (2017)
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(1–2), 195–216 (2018)
Sun, M., Bai, Q.G.: A new descent memory gradient method and its global convergence. J. Syst. Sci. Complex. 24(4), 784–794 (2011)
Sun, M., Liu, J.: Three derivative-free projection methods for nonlinear equations with convex constraints. J. Appl. Math. Comput. 47, 265–276 (2015)
Sun, M., Tian, M.Y., Wang, Y.J.: Multi-step discrete-time Zhang neural networks with application to time-varying nonlinear optimization. Discrete Dyn. Nat. Soc. Article ID 4745759, 1–14 (2019)
Feng, D.X., Sun, M., Wang, X.Y.: A family of conjugate gradient methods for large-scale nonlinear equations. J. Inequ. Appl. 2017, 236 (2017)
Zarantonello, E.H.: Projections on Convex Sets in Hilbert Space and Spectral Theory. Academic Press, New York (1971)
Sun, W.Y., Yuan, Y.X.: Optimization Theory and Methods: Nonlinear Programming. Springer Optimization and Its Applications, vol. 1. Springer, New York (2006)
Zhang, L., Zhou, W.J., Li, D.H.: A descent modified Polak–Ribi$$\grave{\rm e}$$re–Polyak conjugate gradient method and its global convergence. IMA J. Numer. Anal. 26, 629–640 (2006)
Zhang, L., Zhou, W.J., Li, D.H.: Global convergence of a modified Fletcher–Reeves conjugate method with Armijo-type line search. Numerische Mathematik 104, 561–572 (2006)
Solodov, M.V., Svaiter, B.F.: A globally convergent inexact Newton method for systems of monotone equations. In: Fukushima, M., Qi, L. (eds.) Reformulation: Nonsmooth, Semismooth and Smoothing Methods, Piecewise smooth, pp. 335–369. Kluwer Academic Publishers, Dordrecht (1998)
Polyak B.T.: Introduction to Optimization. Optimization Software Inc., Publications Division, New York (1987) (Translated from Russian, with a foreword by Dimitri P. Bertsekas)
Tibshirani, R.: Regression shrinkage and selection via the LASSO. J. R. Stat. Soc. Ser. B Stat. Methodol. 58, 267–288 (1996)
Wu, L., Sun, Z.: New nonsmooth equations-based algorithms for $$\ell _1$$-norm minimization and applications. J. Appl. Math. 139609, 1–14 (2012)