Xiaoqi Yang (杨晓琪)
Professor at Department of Applied Mathematics, Hong Kong Polytechnic University
Professor Yang received his BSc degree in Mathematics from the Chongqing University, Chongqing, a MSc degree in Operations Research and Control Theory from the Institute of System Science at Chinese Academy of Science, Beijing, and a PhD degree in Applied Mathematics at University of New South Wales, Sydney. He then spent five years at the School of Mathematics and Statistics in the University of Western Australia as a Research Associate (1994-1996), an Australian Research Council postdoctoral fellow (1997) and a lecturer (1998). Since 1999 he has been with the Department of Applied Mathematics, Hong Kong Polytechnic University, as an Assistant Professor (1999-2001), Associate Professor (2002-2004), Professor (2005- ). He has presented plenary and invited talks in many international conferences including in Annual Meeting of Chinese Society of Operations Research, Xuzhou Normal university 2014. He has been in editorial boards in several international journals, including Journal of Optimization Theory and Applications. In 2000 he received the ISI Citation Classic for the paper "The vector complementary problem and its equivalences with the weak minimal element in ordered spaces", Journal of Mathematical Analysis and Applications, Vol. 153 (1990) pp. 136-158. In 2006 he received The First Prize of Natural Science from the Chongqing Municipal Government. In 2000 and 2017 he received the President's Award for Outstanding Performance / Achievement in the category of Research and Scholarly Activities, Hong Kong Polytechnic University respectively.
Research Interests:
Vector variational inequalities and vector complementarity problems, nonsmooth analysis, nonlinear optimization, vector optimization, financial optimization, stability analysis, sparse optimization.
The Research Monographs:
Goh C.J. and Yang X.Q. Duality in Optimization and Variational Inequalities. CRC Press 2002
Rubinov A. and Yang X.Q. Lagrange-type Functions in Constrained Nonconvex Optimization. Kluwer 2003
Chen G.Y., Huang X.X. and Yang X.Q. Vector Optimization: Set-Valued and Variational Analysis. Springer 2005
Selected Publications (Full publications list):
Vector variational inequalities and vector complementarity problems:
Chen, G.Y. and Yang, X.Q., The vector complementary problem and its equivalences with the weak minimal element in ordered spaces, Journal of Mathematical Analysis and Applications, Vol. 153 (1990) 136-158.
Yang, X.Q., Vector variational inequalities and its duality, Nonlinear Analysis — The- ory, Method and Applications, Vol. 21, (1993) 867-877.
Yang, X.Q., Vector complementarity and minimal element problems, Journal of Op- timization Theory and Applications. Vol. 77, No. 3 (1993) 483-495.
Yang, X.Q., Generalized convex functions and vector variational inequalities, Journal of Optimization Theory and Applications, Vol. 79, No. 3 (1993) 563-580.
Yang, X.Q. and Goh, C.J., On vector variational inequality. application to vector equilibria. Journal of Optimization Theory and Applications Vol. 95 (1997) pp. 431- 443.
Nonsmooth analysis:
Yang, X.Q. and V. Jeyakumar, Generalized second-order directional derivatives and optimization with C^{1,1} functions, Optimization, Vol. 26 (1992) 165-185.
Yang, X.Q., Second-order conditions of C^{1,1} optimization with applications, Numerical Functional Analysis and Optimization, Vol. 14 (5&6) (1993) 621-632.
Yang, X.Q., Generalized second-order directional derivatives and optimality conditions, Nonlinear Analysis - Theory, Method and Applications, Vol. 23, (1994) 767-784.
Yang, X.Q., An exterior point method for computing points that satisfy second-order necessary conditions for a C^{1,1} optimization problem, Journal of Mathematical Analysis and Applications, Vol. 186, (1994) 118-133.
Yang, X.Q., On second-order directional derivatives, Nonlinear Analysis - Theory, Methods and Applications, Vol. 26 (1996) 55-66.
Nonlinear optimization:
Rubinov, A.M., Glover B.M. and Yang X.Q., Decreasing functions with applications to penalization, SIAM Journal on Optimization Vol. 10, No. 1, (1999) pp. 289-313.
Huang X.X., and Yang, X.Q., A unified augmented Lagrangian approach to duality and exact penalization, Mathematics of Operations Research Vol. 28 (2003), no. 3, 533–552.
Yang X.Q. and Meng Z.Q., Lagrange multipliers and calmness conditions of order p, Math. Oper. Res. Vol. 32 No. 1 (2007) pp. 95-101.
Meng K.W. and Yang X.Q., Optimality conditions via exact penalty functions, SIAM J. Optimiz. Vol. 20, (2010) No. 6, pp. 3208-3231.
Vector optimization:
Jeyakumar, V. and Yang, X.Q., Convex composite multi-objective nonsmooth pro- gramming, Mathematical Programming, Vol. 59 (1993) 325-343.
Yang X.Q., Second-order global optimality conditions for convex composite optimization, Mathematical Programming Vol. 81 (1998) pp.327-347.
Huang X.X. and Yang X.Q. Nonlinear Lagrangian for multiobjective optimization and applications to duality and exact penalization SIAM J. Optimization, Vol. 13, no. 3, pp. 675-692, 2002.
Chen G.Y. and Yang X.Q., Characterizations of variable domination structures via a nonlinear scalarization. Journal of Optimization Theory and Applications Vol. 112, (2002) pp. 97-110.
Wang J.H., Hu Y.H., Yu C.K.W., Li C. and Yang X.Q. Extended Newton methods for multiobjective optimization: majorizing function technique and convergence analysis. SIAM J. Optimization, Vol. 29, No. 3, pp. 2388--2421 2019.(pdf)
Zheng X.Y. and Yang X.Q. Fully piecewise linear vector optimization problems (pdf)
Financial optimization:
Cai X.Q., Teo K.L., Yang X.Q. and Zhou X.Y., Portfolio optimization under a minimax rule, Management Science, Vol. 46 (2000) pp. 957-972.
Wang S., Yang X.Q. and Teo K.L., A power penalty method for a linear complemen- tarity problem arising from American option valuation. J. Optim. Theor Appl. Vol. 129, (2006) No. 2, pp. 227-254.
Zhang K., Yang X.Q. and Teo K.L., Augmented Lagrangian method applied to American option pricing, Automatica J. IFAC. Vol. 42, (2006) No. 8, pp. 1407-1416.
Fang Y.P., Meng K. W. and Yang X.Q., Piecewise linear multi-criteria Programs: the continuous case and its discontinuous generalization. Oper. Res. Vol. 60, (2012) pp. pp. 398-409.
Zhang K., Yang X.Q. and Hu Y.H., Power penalty method for solving HJB equations arising from finance. Automatica J. IFAC. (2020).
Stability analysis:
Meng, K.W., Yang, X.Q.: Equivalent conditions for local error bounds. Set-Valued Var. Anal. 20(4), 532 617–636 (2012)(pdf)
Li M.H., Meng K.W. and Yang X.Q. On error bound moduli for locally Lipschitz and regular functions. Mathematical Programming A Vol. 171 (2018) no. 1-2, pp. 463-487. (pdf)
Kruger, A., Lopez, M., Yang X.Q. and Zhu, J.X.. Holder error bounds and Holder calmness with applications to convex semi-infinite optimization(pdf)
Li M.H., Meng K.W., Yao W.F. and Yang X.Q. Lipschitz-like property relative to a set and the generalized Mordukhovich criterion. Mathematical Programming B (pdf)
Sparse optimization:
Hu Y.H., Li C., Meng K.W., Qin J. and Yang X.Q. Group sparse optimization via L_{p,q} regularization. J. Mach. Learn. Res. 18 (2017), Paper No. 30, 52 pp. (pdf)
Li X., Hu Y.H., Li C., Yang X.Q. and Jiang T.Z., Sparse estimation via lower-order optimization methods in high-dimensional linear regression (pdf)
Hu Y.H., Li C., Meng K.W. and Yang X.Q., Linear convergence of inexact descent method and inexact proximal gradient algorithms for lower-order regularization problems. Journal of Global Optimization.
Recent Research Projects from the Hong Kong government (Full research grants list)):
The Lipschitz-like Property Relative to a Set with Applications (1.2021 - 12.2023) (abstract)
Stability Analysis of Generalised Equations with Applications (1.2020 - 12.2022) (abstract)
Error Bounds and their Stability Analysis and Applications (1.2019 - 12.2021) (abstract)
Variational Analysis of Piecewise Linear Vector Optimization (1.2018 - 12.2020) abstract)
Linearized proximal algorithms with Bregman distance for convex composite optimization with applications (1.2017 - 12.2019) (abstract)
Nonlinear Constrained Sparse Optimization with Lower Order Regularization (1.2016 - 12.2018) (abstract)
Conference talks:
First- and Second-Order Necessary Conditions via Lower-order Exact Penalty Functions (pdf)
Lower-order Regularization for Sparse Optimization with Applications (pdf)
On Error Bound Moduli for Locally Lipschitz and Regular Functions (pdf)
Lagrange-type Functions with Applications (pdf)
Piecewise Multicriteria Programs with Applications in Finance (pdf)
Group sparse optimization via L_{p,q} regularization (pdf)
A List of References for Vector Variational Inequalities
I am looking for excellent MSc students with mathematics and applied mathematics background in pursuing PhD study in my research group. If you are interested, you are welcome to contact me by email (mayangxq at polyu.edu.hk).
Contact details:
Co-group leader of the research group "Applied Optimization and Operations Research"
Program leader for Master of Science in Applied Mathematics for Science and Technology Specialisms: i. Actuarial and Investment Science and ii. Decision Science
Telephone: (852) 2766 6954 Fax: (852) 2362 9045 E-mail: mayangxq at polyu.edu.hk
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
