Quantitative Stability Analysis of Stochastic Generalized Equations

Quantitative Stability Analysis of Stochastic Generalized Equations

Publications
  1. Yongchao Liu, Werner Roemisch and Huifu Xu,

Quantitative Stability Analysis of Stochastic Generalized Equations.

To appear in SIAM J. Optimization.

  1. 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.

  1. 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
  2. Arash Gourtani, David Pozo, Maria Teresa Vespucci and Huifu Xu,

Medium-Term Trading Strategy of a Dominant Electricity Producer.

Energy Systems. December 2013

  1. 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.

  1. 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

To appear in Journal of Optimization Theory and Applications. Online publication 2012.

  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, online publication 2013.

  1. D. Zhang and H. Xu,

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

Optimization, 2011.

  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.

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:

  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

Y. Liu and H. Xu, Entropic approximation for mathematical programs with robust equilibrium constraints, August 2013, submitted.

H. Sun and H. Xu, Asymptotic Convergence Analysis for Distributional Robust Optimization and Equilibrium Problems, May 2013, Optimization online

E. Anderson, H. Xu and D. Zhang, CVaR Approximations for Minimax and Robust Convex Optimization, May 2013, Optimization online,

Yongchao Liu, Werner Roemisch and Huifu Xu,

Quantitative Stability Analysis of Stochastic Generalized Equations

Optimization online, June, 2012.

revised in September 2013

\\Samba0\homes\public_html\research\Published\2013\SGE-SIAM-R2-6-Sept-2013.pdf

H. Xu

Level function method for abstract convex programming.

Manuscripts, School of Information Technology and Mathematical Sciences, University of Ballarat, Australia, 1998 (unpublished).

Top View