Recent Preprints

  1. On the Lidskii--Vishik--Lyusternik perturbation theory for eigenvalues of matrices with arbitrary Jordan structure, with J. Moro and M. L. Overton, in SIAM J. Matrix Anal. Appl., 18(1997), 793--817.
  2. A variable metric proximal point algorithm for monotone operators , with M. Qian, to appear in SIAM J. Control and Optimization (submitted August 1992).
  3. On the super--linear convergence of the variable metric proximal point algorithm using Broyden and BFGS matrix secant updating, with M. Qian, to appear in Mathematical Programming (submitted August 1996). (for the PDF version click here)

    (click here for galley corrections in postscript)

    (click here for galley corrections in PDF)

  4. Limited memory BFGS updating in a trust--region framework, with A. Wiegmann and Linag Xu, July 1996 (updated 2008).
  5. A polynomial time interior--point path--following algorithm for LCP based on Chen--Harker--Kanzow smoothing techniques, with Song Xu, to appear in Mathematical Programming, 86(1999), 91-103.
  6. The global linear convergence of a non--interior path--following algorithm for linear complementarity problems, with S. Xu, to appear in Mathematics of Operations Research, 23(1999), 719-734.
  7. A non--interior predictor--corrector path following algorithm for the monotone linear complementarity problem with S. Xu, Mathematical Programming, 87(2000), 113-130.
  8. A non--interior predictor--corrector path following method for LCP with S. Xu, to appear in a special volume Reformulation-- Nonsmooth, Piecewise Smooth, Semi--smooth, and Smoothing Methods, by Kluwer Academic Publishers, edited by Liqun Qi and Masao Fukushima, 1998.
  9. On the local super-linear convergence of a matrix secant implementation of the variable metric proximal point algorithm for monotone operators, with M. Qian, to appear in a special volume Reformulation-- Nonsmooth, Piecewise Smooth, Semi--smooth, and Smoothing Methods, by Kluwer Academic Publishers, edited by Liqun Qi and Masao Fukushima, 1998.
  10. The Complexity of a Non-Interior Path Following Method for the Linear Complementarity Problem, with S. Xu, JOTA, 112(2002).
  11. Variational Analysis of Non-Lipschitz Spectral Functions, with Michael Overton, Mathematical Programming, 90(2001), 317-351. September 1999.
  12. Optimizing Matrix Stability, with Adrian lewis and Michael Overton, Proceedings of the AMS, 129(2000), 1635-1642.
  13. Variational analysis of the abscissa mapping for polynomials, with Michael Overton, SIAM J. Control and Optimization, 39(2000), 1651-1676.
  14. Optimal stability and eigenvalue multiplicity, with Adrian lewis and Michael Overton, Frontiers of Computational Mathematics, 1(2001), 205-225.
  15. Weak sharp minima revisited, part I: basic theory, with Sien Deng, Control & Cybernetics, 31(2002), 439-469. ERRATA
  16. Approximating subdifferentials by random sampling of gradients, with Adrian lewis and Michael Overton, Mathematics of Operations Research, 27(2002), 567--584.
  17. Two numerical approaches to optimizing matrix stability, with Adrian lewis and Michael Overton, Linear Algebra and Its Applications, 351-352(2002), 117--145.
  18. Optical wavefront reconstruction: theory and numerical methods , with Russell Luke, SIAM Review, 44(2002), 169--224.
  19. Weak sharp minima revisited, part II: application to linear regularity and error bounds, with Sien Deng, Mathematical Programming, Online First, DOI: 10.1007/s10107-005-0615-2.
  20. A sequential quadratic programming method for potentially infeasible mathematical programs,