Publications

 

1.     E. Anderson, H. Xu and D. Zhang

Varying confidence levels for CVaR risk measures and minimax limits.

Mathematical Programming Series A.

2.     A. Pichler and H. Xu

 Quantitative stability analysis for minimax distributionally robust risk optimization.

Mathematical Programming Series B.

3.     S. Guo and H. Xu

Distributionally robust shortfall risk optimization model and its approximation.

            Mathematical Programming Series B, https://doi.org/10.1007/s10107-018-1307-z.

4.     M. Battarra, B. Balcik and H. Xu

 Disaster preparedness using risk-assessment methods from earthquake engineering.

European Journal of Operational Research. DOI: 10.1016/j.ejor.2018.02.014

5.     X. Chen, H. Sun and H. Xu

Discrete approximation of two-stage stochastic and distributionally robust linear complementarity problems.

Mathematical Programming series A, https://link.springer.com/article/10.1007/s10107-018-1266-4.

6.     Y. Liu, A. Pichler and H. Xu

Discrete Approximation and Quantification in Distributionally Robust Optimization.

 Mathematics of Operations Research, 2018.

7.     Y. Liu, H. Xu, S. Yang and J. Zhang

 Distributionally Robust Equilibrium for Continuous Games: Nash and Stackelberg Models.

European Journal of Operations Research, Vol. 265, pp. 631-643, 2018.

8.     H. Xu, Y. Liu and S. Sun

 Distributionally Robust Optimization with Matrix Moment Constraints: Lagrange Duality and Cutting Plane Methods.

Mathematical Programming Series A, http://link.springer.com/article/10.1007/s10107-017-1143-6,Vol. 169, pp. 489-529,  2018.

9.     J. Zhang, H. Xu and L.W. Zhang

 Quantitative Stability Analysis of Stochastic Quasi-Variational Inequality Problems and Applications. 

Mathematical Programming Series B, Vol. 165, pp: 433-470, 2017.

10.  Y. Liu, R. Meskarian and H. Xu

 Distributionally Robust Reward-Risk Ratio Optimization with Moments Constraints.   

SIAM J. Optimization, Vol. 27, No. 2, pp. 957-985, 2017.

11.  S. Guo, H. Xu and L. Zhang 

Convergence Analysis for Mathematical Programs with  Distributionally Robust Chance Constraint.

SIAM J. Optimization, Vol. 27, No. 2, pp. 784–816, 2017.

12.  X. Tong, H. Xu, F. Wu, and Z. Zhao

Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system.

Computational Management Science, 1-30. DOI: 10.1007/s10287-016-0251-8

13.  J. Zhang, H. Xu and L.W. Zhang

Quantitative Stability Analysis for Distributionally Robust Optimization with Moment Constraints. 

SIAM J. Optimization, Vol. 26, pp. 1855-1882, 2016.

14.  S. Guo, H. Xu and L. Zhang

Probability Approximation Schemes for Stochastic Programs with Distributionally Robust Second Order Dominance Constraints.

Optimization Methods and Software, 2016.

15.  A. Gourtani, H. Xu, D. Pozo and T. Nguyen

 Robust Unit Commitment with n-1 Security Criteria

Mathematics Methods of Operations Research, 2016.

16.  H. Sun and H. Xu

 Convergence Analysis for Distributional Robust Optimization and Equilibrium Problems

Mathematics of Operations Research, Vol. 41, pp. 377-401, 2015.

17.  Y. Liu and H. Xu

 Entropic approximation for mathematical programs with robust equilibrium constraints.

SIAM J. Optimization, Vol.  24, pp. 933–958, 2014.

18.  Yongchao Liu, Werner Roemisch and Huifu Xu,

Quantitative Stability Analysis of  Stochastic Generalized Equations.

SIAM J. Optimization. Vol. 24, pp. 467-497, 2014.

19.  Hailin Sun, Huifu Xu, Rudabeh Meskarian and Yong Wang,

Exact Penalization, Level Function Method and Modified Cutting-Plane Method for Stochastic Programs with Second Order Stochastic Dominance Constraints.

SIAM J. Optimization, Vol. 23, pp. 602-631, 2013.

20.  H. Sun, H. Xu and Y. Wang,

A Smoothing  Penalized Sample Average Approximation Method for Stochastic Programs with Second Order Stochastic Dominance Constraints

Asian Pacific Journal of Operations Research,  Vol. 30, No. 3, June 2013

21.  Arash Gourtani, David Pozo, Maria Teresa Vespucci and Huifu Xu,

Medium-Term Trading Strategy of a Dominant Electricity Producer.

 Energy Systems. December 2013 http://link.springer.com/article/10.1007/s12667-013-0105-1

22.  Y. Liu and H. Xu

Stability and Sensitivity Analysis of Stochastic Programs with Second Order Dominance Constraints.

Mathematical Programming Series A, Vol. 142, pp. 435-460, 2013.

23.  H. Xu and D. Zhang

Stochastic Nash equilibrium problems: sample average approximation and applications.

Computational Optimization and Applications,  Vol. 55, pp. 597-645, 2013.

  1. Hailin Sun, Huifu Xu and Yong Wang

Asymptotic Analysis of Sample Average Approximation for Stochastic Optimization Problems with Joint Chance Constraints via CVaR/DC Approximations

Journal of Optimization Theory and Applications. Vol. 161, pp. 257-284, 2014.

  1. H. Sun and H. Xu

Convergence Analysis of Stationary Points in Sample Average Approximation of Stochastic Programs with Second Order Stochastic Dominance Constraints

 Mathematical Programming Series A, Vol. 143, pp. 489-529, 2014.

  1. D. Zhang and H. Xu,

     Two stage stochastic equilibrium problems with equilibrium constraints: modeling  and numerical schemes

Optimization, Vol. 62, pp. 1627-1650, 2013.

  1. Yongchao Liu, Huifu Xu and Guihua Lin

Stability Analysis of One Stage Stochastic Mathematical Programs with Complementarity Constraints

Journal of Optimization Theory and Applications, Vol. 152, pp. 573-555, 2012.

  1. R. Meskarian, H. Xu and J. Fliege

      Numerical Methods for Stochastic Programs with Second Order Dominance Constraints with Applications to Portfolio Optimization

          European Journal of Operational Research, 2011.

  1. Y. Liu, H. Xu and J. J. Ye,

           Penalized Sample Average Approximation Methods for Stochastic Mathematical Programs with Complementarity Constraints

Mathematics of Operations Research, Vol.36, No. 4, pp. 670-694, 2011.

  1. H. Xu and H. Sun

      A note on uniform exponential convergence of sample average approximation of random functions,

      Journal of Mathematical Analysis and Applications, Vol. 385, pp. 698-708, 2011.

  1. D. Ralph and H. Xu

Convergence  of Stationary Points of  Sample Average Two Stage Stochastic Programs:  A Generalized Equation Approach

Mathematics of Operations Research, Vol. 36, No. 3, pp. 568-592, 2011.

  1. J. Fliege and H. Xu

     Stochastic multiobjective optimization: sample average approximation and applications.

Journal of Optimization Theory and Applications, Vol. 151, 2011.

  1. Y. Liu, H. Xu and G.H. Lin

           Stability Analysis of Two Stage Stochastic Mathematical Programs with Complementarity Constraints via NLP-Regularization.

      SIAM Journal on Optimization,Vol. 21, No. 3, pp. 609-705, 2011.

  1. H. Xu and J. J. Ye

      Approximating Stationary Points of  Stochastic Mathematical Programs with Variational Inequality Constraints via Sample Averaging.

    http://www.springerlink.com/content/5622m6138q878826/fulltext.pdf

     Set-Valued and Variational Analysis, Vol. 19, pp. 283-309, 2011.

  1. H. Xu and D. Zhang

      Monte Carlo Methods for Mean-Risk Optimization and Portfolio Selection.  

     Computational Management Sciences, 2010.

  1. H. Xu

      Uniform Exponential Convergence of Sample Average Random Functions under General Sampling with Applications in Stochastic Programming.

      Journal of Mathematical Analysis and Applications, Vol.368,  pp.692-710,  2010.

  1. H. Xu and J.J. Ye

      Necessary Optimality Conditions for  two-stage Stochastic  Programs with Equilibrium Constraints

      SIAM J. Optimization, Vol. 20, pp. 1685-1715, 2010.

  1. H. Xu

      Sample average approximation methods for a class of stochastic variational inequality problems.

       Asian Pacific Journal of Operations Research,  Vol. 27,  pp. 103-119, 2010 (Special issue edited by W. Sun, T. Tanino and H. Xu )

  1. D. Zhang, H. Xu and Y. Wu

      A two stage stochastic equilibrium model for electricity markets with two way contracts.

      Mathematical Methods of Operations Research, Vol. 71, pp. 1-45,  2010.

  1. D. Zhang, H. Xu and Y. Wu,

      Single and multi-Period Optimal Inventory Control Models with Risk-Averse Constraints

      European Journal of Operations Research, Vol. 199, pp. 420–434, 2009.

  1. V. DeMiguel and H. Xu  

      A Stochastic Multiple Leader Stackelberg Model: Analysis, Computation, and Application

     Operations Research, Vol. 57, No. 5, pp. 1220–1235 2009.  (supplementary material)

  1. R. Balaji and H. Xu

      Approximating stationary points of stochastic optimization problems in Banach space.

      Journal of Mathematical Analysis and Applications, Vol. 347, pp. 333-343, 2008.

  1. H. Jiang and H. Xu

      Stochastic Approximation Approaches to the Stochastic Variational Inequality Problem.

      IEEE Transactions on Automatic Control, Vol. 53,  pp. 1462-1475, 2008.

  1. H. Xu,  D. Zhang

            Smooth Sample Average Approximation of Stationary Points in Nonsmooth Stochastic Optimization and Applications.

            Mathematical Programming, series A,  Vol 119, 2009, 371-401.

  1. Shapiro and H. Xu

      Stochastic Mathematical Programs with Equilibrium Constraints, Modeling and Sample Average Approximation.

     Optimization, Vol. 57, pp. 395-418, 2008. (Optimization: free access to selected 2008 articles: http://www.tandf.co.uk/journals/pdf/freeaccess/gopt.pdf)

  1. G.H. Lin, H. Xu and M. Fukushima

      Monte Carlo and quasi-Monte Carlo sampling methods for a class of stochastic mathematical programs with equilibrium constraints

      Mathematical Methods of Operations Research, Vol. 67, pp. 423-441, 2008.

  1. F. Meng and H. Xu

           Exponential Convergence of Sample Average Approximation Methods for a Class of Stochastic Mathematical Programs with Complementarity Constraints

            Journal of Computational Mathematics, Vol. 24, pp. 733-748, 2006.

  1. H. Xu and F. Meng

      Convergence analysis of sample average approximation methods for a class of stochastic mathematical programs with equality constraints

       Mathematics of Operations Research, Vol. 32, No. 3, pp. 648-668, 2007.

  1. Shapiro and H. Xu

      Uniform Laws of Large Numbers for Set-Valued Mappings and Subdifferentials of Random Functions.

     Journal of Mathematical Analysis and Applications, Vol.325,  pp. 1390-1399, 2007.

  1. F. Meng and H. Xu

           A Regularized Sample Average Approximation Method for Stochastic Mathematical Programs with Nonsmooth Equality Constraints

            SIAM Journal on Optimization, Vol. 17, pp. 891-919, 2006.

  1. H. Xu

            An implicit programming approach for a class of stochastic mathematical programs with complementarity constraints

            SIAM Journal on Optimization, Vol.16, PP. 670-696, 2006.

  1. E. Anderson, A. B. Philpott and H. Xu

      Modelling the effects of interconnection between electricity markets.

      Mathematical Methods of Operations Research, Vol. 65, pp.1-26, 2007.

  1. E. Anderson and H. Xu

      Optimal supply functions in electricity markets with option contracts and nonsmooth costs.

      Mathematical Methods of Operations Research, Vol. 63, No. 3, pp. 387-411, 2006.

  1. E. Anderson and H. Xu 

      Epsilon-optimal bidding in electricity markets with discontinuous market distribution function.

      SIAM Journal on Control and Optimization, Vol. 44, pp.1391-1418, 2005.

  1. H. Xu

      An MPCC approach for stochastic Stackelberg-Nash-Cournot Equilibrium,

      Optimization, Vol. 54, pp. 27-57, 2005.

  1. D. Ralph and H. Xu

      Implicit smoothing and its application to optimization with piecewise smooth equality constraints.

      Journal of Optimization Theory and Applications, Vol. 124, No. 3, 2005.

  1. E. Anderson and H. Xu

      Contracts and supply functions in electricity.

      Journal of Optimization Theory and Applications, Vol. 124, No. 2, pp. 257-283, 2005.

  1. E. Anderson and H. Xu

      Nash equilibria in electricity markets,

      Mathematical Methods of Operations Research, Vol. 60, pp. 215-238, 2004.

  1. H. Xu

     Point-based set-valued approximation, C-differentiable operator and application,

     Optimization, Vol. 52,  pp. 127-143, 2003.

  1. E. Anderson and H. Xu 

      Nash equilibria in electricity markets with fixed prices points,

      Optimization and Industry: New Frontiers, Panos Pardalos and Victor Korotkich eds, Kluwer Academic Publishers, pp. 141-157, 2003.

  1. E. Anderson and H. Xu

      Necessary and sufficient conditions for optimal offers in electricity markets,

      SIAM Journal on Control and Optimization, Vol. 41, pp. 1212-1228, 2002.

  1. S. Sheng and H. Xu

      Picard iteration for nonsmooth equations,

     Journal of Computational Mathematics, Vol. 19, No. 6, pp. 583-590, 2001.

  1. H. Xu

     Adaptive smoothing method, deterministically computable generalized Jacobians and Newton's method.

    Journal of Optimization Theory and Applications, Vol. 109, No. 1, pp. 215-224, 2001.

  1. H. Xu

     Regularized gap functions and D-gap functions for nonsmooth variational inequalities.

    Optimization and Related Topics, A. Rubinov and B. Glover eds., Kluwer Academic Publishers, 2001.  pdf

  1. H. Xu

      Level function of some optimal value function

     Optimization and Related Topics, A. Rubinov and B. Glover eds., Kluwer Academic Publishers, 2001. pdf

  1. H. Xu

      Level function method for quasi-convex programming

      Journal of Optimization Theory and Applications, Vol. 108, No. 2, 2001.pdf

  1. H. Xu, A. Rubinov and B. M. Glover

     Continuous approximations to generalized Jacobians.

      Optimization, Vol. 46, pp. 221--246, 1999. pdf

  1. H. Xu A. Rubinov and B. M. Glover

     Approximations to the Clarke generalized Jacobian and nonsmooth least-squares minimization

     Progress in Optimization: Contribution from Australasia, E. Eberhard et al eds., Kluwer Academic Publishers, pp. 193--210, 1999. pdf

  1. H. Xu

      Set-valued approximation and Newton's methods

      Mathematical Programming, Vol. 84, No. 2, 1999, pp. 401-420.pdf

  1. H. Xu, A. Rubinov and B. M. Glover

           Strict lower sub-differentiability and application.

           Journal of the Australian Mathematical Society, Series B, Vol. 40, 1999,

           pp. 379-391. pdf

  1. M. Y. Andramonov, B. M. Glover, A. M. Rubinov and H. Xu

      Numerical methods for abstract convex programming,

      Optimization Techniques and Applications (International Conference on Optimization Techniques and Applications), Curtin University,

      L. Caccetta et al eds., Vol. 1, pp. 229-234, 1998

  1. H. Xu and B. M. Glover

      New version of Newton's method for nonsmooth equations.

     Journal of Optimization Theory and Applications, Vol. 93, pp. 395-414, 1997.pdf

  1. H. Xu and Xiaowen Chang

      Approximate Newton methods for nonsmooth equations

      Journal of Optimization Theory and Applications, Vol. 93,  pp. 373-394, 1997.pdf

  1. H. Xu

     On the extension of minimization algorithms from convex to lower sub-differentiable problems

     Proceedings of the Optimization Mini-conference III, B. M. Glover, B. D. Craven and D. Ralph eds.,  University of Melbourne, pp. 13-23, 1996.

  1. H. Xu

      Stochastic penalty function methods for nonsmooth constrained minimization.

      Journal of Optimization Theory and Applications, Vol. 88,  pp. 709-724, 1996.pdf

  1. H. Xu

      A sufficient condition for nonlinear nonconvex L1-minimization.

     Journal of Ningbo University, 1996.

  1. H. Xu

      Non-descent sub-gradient method for nonsmooth constrained minimization,

      Numerical Mathematics, A Journal of Chinese Universities, English Series. Vol. 3, No 2. 1994. pdf

  1. H. Xu

      L1-penalty function method for nonsmooth equality and inequality constrained minimization.

      Journal of Ningbo University, Vol. 7, No 2. 1994.

  1. H. Xu

      Some remarks on collinear scaling methods for unconstrained minimization.

      Journal of Ningbo University, Vol. 7, No. 1, 1994.

  1. H. Xu

      Penalty function method for a class of nonsmooth nonlinear programming problems.

       Journal of Ningbo University, Vol 5, No. 2, 1992.

  1. H. Xu

      L1-Exact penalty function method for non-differentiable constrained minimization

     Journal of Ningbo University, Vol. 5, No. 1, 1992.

  1. H. Xu and Sheng Shongbai

      Broyden family of collinear scaling algorithm for unconstrained optimization.

     Numerical Mathematics, A  Journal of Chinese Universities, Vol. 13, No. 4, 1991.

  1. H. Xu,

      On the convergence of inexact Newton Method at singular points.

      Journal of Ningbo University, Vol. 3, No.1, 1990.

 

Mathematical Review of my papers

 

Reports and Manuscripts

 

 

S. Guo, H. Xu and L. Zhang, Continuous Behavioural functions equilibria and approximation schemes in Bayesian games with non-finite type and action spaces, arXiv:1710.04968, 2017.

Under revision

 

 

E. Delage, S. Guo and H. Xu, Shortfall risk models when information of loss function is incomplete, Optimization online, April 2018.

 

W. Haskell, W. Huang and H. Xu, Preference Elicitation and Robust Optimization with Multi-Attribute Quasi-Concave Choice Functions, arXiv:1805.06632, 2018. Under revision.

 

Y. Chen, H. Sun and H. Xu,

Decomposition Methods for Solving Two-Stage Distributionally Robust Optimization Problems, Optimization-online, 2018.

H. Xu

Level function method for abstract convex programming.

Manuscripts, School of Information Technology and Mathematical Sciences, University of Ballarat, Australia, 1998 (unpublished).