Publications

· A revisit on Landweber iteration (with Roimmel Real), preprint 2020.

· A note on non-ergodic convergence rate of alternating direction method of multipliers, preprint 2020.

· Heuristic discrepancy principle for variational regularization of inverse problems (with H. Liu, R. Real, X. Lu, X. Jia), preprint 2019. PDF,

· Analysis of a heuristic rule for the IRGNM in Banach spaces with convex regularization terms (with Z Fu, Z. Zhang, B Han and Y Chen), Inverse Problems, 2020. Accepted for publication PDF

· Regularization of inverse problems by two-point gradient methods in Banach spaces (with Min Zhong and Wei Wang), Numer. Math., 2019. DOI

· Solving a nonlinear inverse Robin problem through a linear Cauchy problem (with R. F. Gong, P. J. Yu, X. L. Chen, and W. Han), Applicable Analysis, Accepted. DOI

· Heuristic rule for non-stationary iterated Tikhonov regularization in Banach spaces (with Zhengqiang Zhang). Inverse Problems, 34 (2018), no. 11, 115002, 26 pp. DOI

· Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule (with Wei Wang), Inverse Problems, 34 (2018), 035001 (24pp). DOI

· On a heuristic rule for the regularization of inverse problems by the augmented Lagrangian method, Numer. Math., 136 (2017), no. 4, 973—992. DOI

· Preconditioned alternating direction method of multipliers for solving inverse problems with constraints (with Yuling Jiao, Xiliang Lu and Weijie Wang). Inverse Problems, 33 (2017), 025004 (34pp). DOI

· Landweber-Kaczmarz method in Banach spaces with inexact inner solvers, Inverse Problems, 32 (2016), 104005 (26pp). PDF DOI

· Alternating direction method of multipliers for linear inverse problems (with Yuling Jiao, Xiliang Lu and Weijie Wang), SIAM J. Numer. Anal., 54 (2016), no. 4, 2114-2137. PDF DOI

· Levenberg-Marquardt method in Banach spaces with general convex regularization terms (with Hongqi Yang), Numer. Math. 133 (2016), no. 4, 655-684. PDF DOI

· Hanke-Raus heuristic rule for variational regularization in Banach spaces, Inverse Problems, 32 (2016), 085008 (19pp). PDF DOI

· Inexact Newton-Landweber iteration in Banach spaces with non-smooth convex penalty terms, SIAM J. Numer. Anal., 53 (2015), no. 5, 2389--2413. PDF DOI

· Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces (with M. Hegland and W. Wang), Applicable Analysis, 94 (2015), 524--547. PDF DOI

· Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms (with M. Zhong), Numer. Math., 127 (2014), 485--513. PDF DOI

· A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces (with X. Lu), Inverse Problems, 30 (2014), 045012 (21pp). PDF DOI

· Oracle inequality for a statistical Raus-Gfrerer type rule (with P Mathe), SIAM/ASA J. Uncertainty Quantification, 1 (2013), 386—407. PDF DOI

· Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals (with W. Wang), Inverse Problems, 29 (2013), 085011 (22pp). PDF DOI

· On the iteratively regularized Gauss-Newton method in Banach spaces with applications to parameter identification problems (with M Zhong), Numer. Math., 124(2013), 647—683. PDF DOI

· Further convergence results on the iteratively regularized Gauss-Newton methods under the discrepancy principle, Math. Comput., 82 (2013), no. 283, 1647—1665. PDF

· Solving nonlinear inverse problems by evolution equations based on Gauss-Newton methods, Applicable Analysis, 92 (2013), 527--548. PDF

· Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces (with L. Stals), Inverse Problems, 28(2012), 104011(15pp). PDF

· On the order optimality of the regularization via inexact Newton iteration, Numer. Math., 121 (2012), 237—260. PDF

· Inexact Newton-Landweber iteration for solving nonlinear inverse problems in Banach spaces, Inverse Problems, 28(2012), 065002(15pp). PDF

· A general convergence analysis of some Newton type methods for nonlinear inverse problems, SIAM J Numer. Anal., 49 (2011), 549—573. PDF

· Implicit iteration methods in Hilbert scales under general smoothness conditions (with U. Tautenhahn), Inverse Problems, 27(2011), 045012 (27pp). PDF

· Inexact Newton regularization methods in Hilbert scales (with U. Tautenhahn), Numer. Math., 117 (2011), 555--579. PDF

· On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems, Numer. Math., 115 (2010), 229--259. PDF

· On a class of frozen regularized Gauss-Newton methods for nonlinear inverse problems, Math. Comput., 79 (2010), 2191—2211. PDF

· On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems (with U. Tautenhahn), Numer. Math., 111(2009), 509--558. PDF

· A convergence  analysis of the iteratively regularized Gauss-Newton method under Lipschitz condition, Inverse Problems, 24 (2008), 045002(16pp). PDF

· Symmetry and asymmetry: the method of moving spheres (with Yanyan Li and Haoyuan Xu), Advances in Differential Equations, 13 (2008), no. 7-8, 601—640. PDF

· Local Hessian estimates for some conformally invariant fully nonlinearequations with boundary conditions, Differential and Integral Equations, 20 (2007), no. 2, 121--132. PDF

· Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary (with Aobing Li and Yanyan Li), Calculus of Variations and PDEs, 28 (2007), 509--543. PDF

· Starshaped compact hypersurfaces with prescribed k-th mean curvature in hyperbolic space (with Yanyan Li), Discrete Contin. Dyn. Syst., 15 (2006), no. 2, 367—377. PDF

· Nonexistence of Positive solutions for some fully nonlinear Elliptic Equations (with Yanyan Li and Haoyuan Xu), Methods and Applications of Analysis, 12 (2005), no. 4, 441--449. PDF

· Tikhonov regularization and a posteriori rules for solving nonlinear ill posed problems (with U. Tautenhahn), Inverse P roblems, 19 (2003), no. 1, 1--21. PDF

· A discrete scheme of Landweber iteration for solving nonlinear ill-posed problems (With Umberto Amato), J. Math. Anal. Appl., 253 (2001), no. 1, 187--203. PDF

· Convergence of the Red-TOWER method for removing noise from data (with Umberto Amato), IEEE Transaction on Signal Processing. 49(2001), no. 9, 1931--1939. PDF

· On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems, Math. Comput.. 69 (2000), no. 232, 1603--1623. PDF

· The analysis of a discrete scheme of the iteratively regularized Gauss-Newton method, Inverse Problems, 16 (2000), no. 5, 1457--1476. PDF

· Error estimates of some Newton-type methods for solving nonlinear inverse problems in Hilbert scales, Inverse Problems, 16 (2000), no. 1, 187--197. PDF

· A unified treatment of regularization methods for linear ill-posed problems, Numer Math. J Chinese Univ. (English Ser.), 9(2000), no. 1, 111--120. PDF

· Converse and saturation results on Tikhonov regularization together with a posteriori parameter choice, Sci China Ser A, 42(1999), no. 11, 1137--1146. PDF

· A convergence analysis for Tikhonov regularization of nonlinear ill-posed problems. Inverse Problems, 15 (1999), no. 4, 1087--1098. PDF

· On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems (with Zongyi Hou). Numer. Math., 83 (1999), no. 1, 139--159. PDF

· Applications of the modified discrepancy principle to Tikhonov regularization of nonlinear ill-posed problems. SIAM J. Numer. Anal. 36 (1999), no. 2, 475--490. PDF

· Asymptotic regularization methods for ill-posed linear problems (with Zongyi Hou). Chinese Ann. Math. Ser. A, 20(1999), no. 3, 365—374.

· A finite dimensional method for solving nonlinear ill-posed problems (with Z. Y. Hou), J. Comput. Math., 17(1999), no.3, 315—326.

· Application of the modified discrepancy principle to Landweber iteration for linear ill-posed problems (with Z. Hou), J. Fudan Univ. Nat. Sci., 37 (1998), no. 5, 635—643.

· On the choice of the regularization parameter for ordinary and iterated Tikhonov regularization of nonlinear ill-posed problems, Inverse Problems, 13 (1997), no. 3, 815—827.

· Maximum entropy method for solving operator equation of the first kind, Science in China Ser. A, 40 (1997), no. 5, 483—493.