研究成果
代表性研究项目
1、国家自然科学基金面上项目：基于SCO方法和SDP/SOCP松弛技术的非凸二次约束二次规划新全局算法与应用研究（12271485），2023.01-2026.12，项目负责人。
2、国家自然科学基金联合基金重点项目：面向工业场景的安全实时网络柔性架构和智能管控研究（U22A2004），2023.01-2026.12，参与，排名第四（4/10）。
3、浙江省自然科学基金/重点项目：基于锥优化松弛和SCO方法的非凸二次约束二次规划新分支割算法研究（批准号LZ21A010003），2021.1-2023.12，项目负责人。
4、国家自然科学基金面上项目：基于交替凸搜索和凸松弛技术的非凸二次规划新全局算法及其在金融中的应用（11871433），2019.01-2022.12，项目负责人。
5、国家自然科学基金面上项目：基于非多余矩阵分离的二次指派问题SDP近似算法与应用（11371324），2014.01-2017.12，项目负责人。
6、国家自然科学基金面上项目：基于SDP和SOS技术的结构全局优化对偶分解算法（11071219）， 2011.1-2013.12，项目负责人。
7、浙江省自然科学基金一般项目：基于 ADM和 SDP技术的非凸二次规划全局算法研究（LY17A010023），2017.1-2019.12，项目负责人。
8、浙江省自然科学基金一般项目：基于锥优化技术的二次指派问题近似算法（LY13A010012），2013.01-2015.12，项目负责人。
9、浙江省自然科学基金一般项目：约束全局最优化增广Lagrangian方法研究（Y7080184），2009.1-2010.12，项目负责人。
10、中国博士后科学基金特别资助项目（第三批）：结构全局优化对偶分解算法及其在投资组合中的应用（201003242），2010.10-2012.12，项目负责人。
11、中国博士后科学基金面上资助项目：多项式优化及其在投资组合中的应用（20090450653）， 2009.7-2010.10，项目负责人。
发表的代表性论文著作 （标注*为通讯作者）
1、Hezhi Luo, Yuanyuan Chen*, Xianye Zhang, Duan Li, and Huixian Wu. Effective algorithms for optimal portfolio deleveraging problem with cross impact. Mathematical Finance, 1–54，March 2023. https://doi.org/10.1111/mafi.12383
2、Huixian Wu，Hezhi Luo*, Xianye Zhang, Haiqiang Qi. An effective global algorithm for worst-case linear optimization under polyhedral uncertainty. Journal of Global Optimization, 1-29, May 2023. https://doi.org/10.1007/s10898-023-01286-9
3、Hezhi Luo*, Huixian Wu，Xianye Zhang, Weiqiang Xu. Effective algorithms for separable nonconvex quadratic programming with one quadratic and box constraints. Computational Optimization and Applications, 1-42, May 2023. https://doi.org/10.1007/s10589-023-00485-0
4、Huixian Wu, Hezhi Luo*, Xianye Zhang, Jianzhen Liu, A new global algorithm for factor-risk-constrained mean-variance portfolio selection. Journal of Global Optimization, 1-32，Aug. 2022. https://doi.org/10.1007/s10898-022-01218-z
5、Hezhi Luo, Xiaodong Ding, Jiming Peng, Rujun Jiang, Duan Li*, Complexity Results and Effective Algorithms for Worst-case Linear Optimization under Uncertainties, INFORMS Journal on Computing, 33(1): 180-197, 2021. https://doi.org/10.1287/ijoc.2019.0941 （UTD24顶级期刊）
6、Xiaodong Ding, Hezhi Luo*, Huixian Wu, Jianzhen Liu. An efficient global algorithm for the worst-case linear optimization under uncertainties via the nonlinear SDP relaxation. Computational Optimization and Applications, 80: 89-120, Aug. 2021.
7、Hezhi Luo*, Sikai Chen, Huixian Wu, A new branch-and-cut algorithm for non-convex quadratic programming via alternative direction method and semidefinite relaxation, Numerical Algorithms, 88:993-1024, 2021.
8、Hezhi Luo, Xiaodi Bai, Gino Lim, Jiming Peng*. New global algorithms for quadratic programming with a few negative eigenvalues based on alternative direction method and convex relaxation. Mathematical Programming Computation, DOI: 10.1007/s12532-018- 0142-9, 11(1): 119-171, Mar. 2019.
9、Hezhi Luo, Xiaodi Bai, Jiming Peng*. Enhancing semidefinite relaxation for quadratically constrained quadratic programming via penalty methods. Journal of Optimization Theory and Applications, DOI: 10.1007/s10957-018-1416-0, 180(3): 964-992, Mar. 2019.
10、Luo，H. Z. , X. L. Sun, D. Li, On the Convergence of Augmented Lagrangian Methods for Constrained Global Optimization, SIAM Journal on Optimization,18(4): 1209-1230,2007.
11、Luo，H. Z. *, H. X. Wu, J. Z. Liu, On Saddle Points in Semidefinite Optimization via Separation Scheme. Journal of Optimization Theory and Applications, 165:113–150, 2015.
12、J. Peng, T. Zhu, H. Z. Luo and K. Ch. Toh, Semi-definite Programming Relaxation of Quadratic Assignment Problems based on Non-redundant Matrix Splitting. Computational Optimization and Applications, 60(1): 171-198,Jan 2015.(SCI: AY7ER，二区)
13、H. X. Wu, Luo，H. Z. *, J. F. Yang, Nonlinear Separation Approach for the Augmented Lagrangian in Nonlinear Semidefinite Programming. Journal of Global Optimization, 59:695-727,2014.(SCI:AK9CW，二区)
14、Luo，H. Z. *, H. X. Wu, J. Z. Liu, Some Results on Augmented Lagrangians in Constrained Global Optimization via Image Space Analysis. Journal of Optimization Theory and Applications, 159(2):360-385, Nov. 2013(SCI:238QB,二区)
15、H. X. Wu, Luo，H. Z. *, X. D. Ding and G. T. Chen, Global Convergence of Modified Augmented Lagrangian Methods for Nonlinear Semidefinite Programming. Computational Optimization and Applications, 56(3):531-558, Dec. 2013. (SCI:255LM,二区)
16、H. X. Wu and Luo，H. Z. *, Saddle points of general augmented Lagrangians for constrained nonconvex optimization. Journal of Global Optimization, 53(4):683-697, Aug. 2012. (SCI: 966JA, 二区)
17、Luo，H. Z. *, H. X. Wu and G. T. Chen, On the Convergence of Augmented Lagrangian Methods for Nonlinear Semidefinite Programming. Journal of Global Optimization, 54(3): 599-618,Nov. 2012. (SCI: 025WH, 二区)
18、Luo，H. Z. *, X. L. Sun, and Y. F. Xu, On the Convergence Properties of Modified Augmented Lagrangian Methods for Mathematical Programming with Complementarity Constraints，Journal of Global Optimization, 46(2):217-232, Feb. 2010.（SCI:541GJ，二区）
19、Luo，H. Z. , G. Mastroeni, and H. X. Wu, Separation approach for augmented Lagrangians in constrained nonconvex optimization, Journal of Optimization Theory and Applications, 144(2): 275-290, Feb. 2010.（SCI:544OC，二区）
20、Luo，H. Z. , X. L. Sun, and Y. F. Xu, Convergence properties of modified and partially-augmented Lagrangian methods for mathematical programs with complementarity constraints, Journal of Optimization Theory and Applications,145(3):489-506,June 2010.（SCI:591KZ，二区）
21、H. Z. Luo, X. L. Sun, H. X. Wu, Convergence properties of augmented Lagrangian methods for constrained global optimization, Optimization Methods and Software,23(5):763-778, 2008. (SCI:349WR)
22、H. Z. Luo, H. X. Wu，On the characterization of preinvex functions, Journal of Optimization Theory and Applications, 138(2): 297-304,2008.(SCI:320II，二区)
23、X. L. Sun, H. Z. Luo, D. Li, Convexification of nonsmooth monotone functions, Journal of Optimization Theory and Applications,132(2):339-351,2007.(SCI:184PR，二区）
24、H. Z. Luo, Z. K. Xu, On characterizations of prequasi-invex functions, Journal of Optimization Theory and Application,120(2):429-439,2004.(SCI:773LB，二区)
25、罗和治，约束全局最优化增广Lagrangian方法及凸化方法，上海大学出版社，ISBN：978-7- 811 18-650-5/G543，2010. （专著）
