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.

Awards: 

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 2000, he received the President's Award for Outstanding Performance / Achievement in the category of Research and Scholarly Activities, The Hong Kong Polytechnic University.  
In 2006, he received The First Prize of Natural Science from the Chongqing Municipal Government.  
In 2016/2017, he received Faculty Awards (Research & Scholarly Activities) from Faculty of Applied Science and Textiles, The Hong Kong Polytechnic University. 
In 2017, he received the President's Award for Outstanding Performance / Achievement in the category of Research and Scholarly Activities, The Hong Kong Polytechnic University.  
Top 2% Scientists Worldwide published by Stanford University.  

Research Interests: 

Stability analysis, Sparse optimization, Financial optimization, Nonsmooth analysis, Nonlinear optimization, Vector optimization, Vector variational inequalities and vector complementarity problems.

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): 

Stability analysis: 
Li M.H., Meng K.W. and Yang X.Q.: Kurdyka-Lojasiewicz inequality and error bounds of D-gap functions for nonsmooth and nonmonotone variational inequality problems (submitted) (pdf) 
Yao W.F. and Yang X.Q.: Relative Lipschitz-like property of parametric systems via projectional coderivative. SIAM Journal on Optimization 33 (2023) No. 3, pp. 2021--2040 (pdf) 
Meng K.W., Li M.H., Yao W.F. and Yang X.Q. Lipschitz-like property relative to a set and the generalized Mordukhovich criterion. Mathematical Programming B, 189 (2021), no. 1-2, 455–489. (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. Set-Valued Var. Anal. 27 (2019), no. 4, 995–1023. (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) 
Meng, K.W., Yang, X.Q.: Equivalent conditions for local error bounds. Set-Valued Var. Anal. 20(4), 532 617–636 (2012)(pdf) 

Sparse optimization: 
Hu Y.H., Lu J., Yang X.Q. and Zhang K.: Mix sparse optimization: theory and algorithm (submitted) (pdf) 
Hu Y.H., Hu X.L. and Yang X.Q., On convergence of iterative thresholding algorithms to approximate sparse solution for composite nonconvex optimization, Mathematical Programming (to appear) (pdf);  
Wu Y., Pan, S. and Yang X.Q. A regularized Newton method for l_q-norm composite optimization problems, SIAM Journal on Optimization 33 (2023) No. 3, pp. 1676-1706 (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. 79 (2021), no. 4, 853–883. (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. Journal of Global Optimization. 85 (2023), no. 2, 315–349. (pdf) 
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) 

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 complementarity 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. Operations Research 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. 111 (2020), 108668, 9 pp.  

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 programming, 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. J. Optim. Theory Appl. 190 (2021), no. 2, 461–490. (pdf) 

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. (ISI Citation Classic Award 2000) 
Yang, X.Q., Vector variational inequalities and its duality, Nonlinear Analysis — Theory, Method and Applications, Vol. 21, (1993) 867-877. 
Yang, X.Q., Vector complementarity and minimal element problems, Journal of Optimization 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. 

Recent General Research Funds (GRF) from the Hong Kong government (Full research grants list)): 

Mixed Contingent Coderivative and Relative Lipschitz-like Property in Banach Spaces (1.2024 - 12.2026) (abstract) 
Relative Stability Analysis for Parametric Optimization Problems (1.2022 - 12.2024) (abstract) 
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: 

A globally convergent regularized Newton method for l_q-norm composite optimization problems (pdf) 
The Lipschitz-like Property Relative to a Set with Applications (pdf) 
Group sparse optimization via l_{p,q} regularization (pdf) 
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)

Teaching: 

AMA4840 Decision Analysis 
AMA532 Investment Science 

My Students

A List of References for Vector Variational Inequalities

I am looking for undergraduate students and MSc students with strong 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@polyu.edu.hk).