曾主持一项国家自然科学青年基金项目，参与多项国家级项目和省部级项目。主要研究兴趣为非线性规划、矩阵优化、金融优化等。已在相关领域的重要期刊(如: SIOPT, SISC, SIMAX,COAP, JGO, JSC, EJOR等)发表数篇论文。 X.J. Jia, X. Liang, C. Shen, and L-H. Zhang. Solving the cubic regularization model by a nested restarting Lanczos method. SIAM J. Matrix Anal. & Appl., 43(2):812-839, 2022.
X.J. Ma, C. Shen, L. Wang, L-H. Zhang, and R-C. Li. A self-consistent-field iteration for MAXBET with an application to multi-view feature extraction. Advances in Computational Mathematic, 48(2):1-34, 2022.
X. Liu, C. Shen, and L. Wang. A dual active-set proximal Newton algorithm for sparse approximation of correlation matrices. Optimization Methods and Software, 37(5):1820-1844, 2022.
C. Shen, X. Liu. Solving nonnegative sparsity-constrained optimization via DC quadratic-piecewise-linear approximations. Journal of Global Optimization, 81(4):1019-1055, 2021.
L-H. Zhang, X.J. Ma, C. Shen. A structure-exploiting nested Lanczos-type iteration for the multi-view canonical correlation analysis, SIAM J. Sci. Comput., 43(4):A2685-A2713, 2021.
C. Shen, Y.L. Wang, W.J. Xue, and L-H. Zhang. An accelerated active-set algorithm for a quadratic semidefinite program with general constraints. Computational Optimization and Applications, 78:1-42, 2021.
C. Shen, W.J. Xue, L-H. Zhang, and B.Y. Wang. An active-set proximal-Newton algorithm for l1 regularized optimization problems with box constraints. Journal of Scientific Computing, 85(3):57, 2020.
L-H. Zhang, W.H. Yang, C. Shen, and J.Q. Ying. An eigenvalue-based method for the unbalanced Procrustes problem. SIAM J. Matrix Anal. Appl., 41(3):957-983, 2020.
C. Shen, C. Fan, Y. Wang, and W. Xue. Limited memory BFGS algorithm for the matrix approximation problem in Frobenius norm. Computational and Applied Mathematics, 39(2):43, 2020.
L-H. Zhang, C. Shen. A nested Lanczos method for the trust-region subproblem. SIAM J. Sci. Comput., 40(4):A2005-A2032, 2018.
L-H. Zhang, C. Shen, W.H. Yang, and J.J. Judice. A Lanczos method for large-scale extreme Lorentz eigenvalue problems. SIAM J. Matrix Anal. & Appl., 39(2):611-631, 2018.
L-H. Zhang, C. Shen, and R-C. Li. On the generalized Lanczos trust-region method. SIAM J. Optim., 27(3):2110-2142, 2017.(“若琳奖”（Distinguished Paper Award） of 2018 ICCM Best Paper Award)
C. Shen, L-H. Zhang, and W.H. Yang. A filter active-set algorithm for ball/sphere constrained optimization problem. SIAM J. Optim. 26(3):1429-1464, 2016.
C. Shen, L-H. Zhang, and W. Liu. A stabilized filter SQP algorithm for nonlinear programming. Journal of Global Optimization， 65:677-708, 2016.
L-H. Zhang, W.H. Yang, C. Shen, and R-C. Li. A Krylov subspace method for large-scale second-Order cone linear complementarity problem. SIAM J. Sci. Comput. 37(4):A2046-A2075, 2015.
C. Shen, L.-H Zhang, B. Wang and W.Q. Shao, Global and local convergence of a nonmonotone SQP method for constrained nonlinear optimization. Computational Optimization and Applications, 59(3):435-473, 2014.
W. Liu, C. Shen, X. Zhu and D. Pu. An infeasible QP-free algorithm without a penalty function or a filter for nonlinear inequality constrained optimization. Optimization Methods and Software, 29(6):1238-1260, 2014.
W. Xue, C. Shen and W. Shao. Convergence analysis of a regularized interior point algorithm for the barrier problems with singular solutions. Linear Algebra and its Applications, 438(13):4654-4671, 2013.
C. Shen, S. Leyffer and R. Fletcher. A nonmonotone filter method for nonlinear optimization. Computational Optimization and Applications, 52:583-607, 2012. (COAP 2012 Best Paper Award)
C. Shen, W. Xue and D. Pu. An infeasible SSLE filter algorithm for general constrained optimization without strict complementarity. Asia-Pacific Journal of Operational Research, 28(3):361-399, 2011.
C. Shen, W. Xue and X.D. Chen. Global convergence of a robust filter SQP algorithm. European Journal of Operational Research, 206(1):34-45, 2010.
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