Elizabeth Wong

teaching

papers

• P. E. Gill, E. Wong.
  Sequential Quadratic Programming Methods.
  in J. Lee and S. Leyffer (eds), Mixed Integer Nonlinear Programming, The IMA Volumes in Mathematics and its Applications, Volume 154, Springer Verlag, Berlin, Heidelberg and New York, 147--224, 2012.
  ( bibtex )

  @incollection {GilW12a,
       AUTHOR = {Gill, Philip E. and Wong, Elizabeth},
  AFFILIATION = {Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA},
        TITLE = {Sequential Quadratic Programming Methods},
    BOOKTITLE = {Mixed Integer Nonlinear Programming},
       SERIES = {The IMA Volumes in Mathematics and its Applications},
       EDITOR = {Lee, Jon and Leyffer, Sven},
    PUBLISHER = {Springer New York},
         ISBN = {978-1-4614-1927-3},
      KEYWORD = {Mathematics and Statistics},
        PAGES = {147-224},
       VOLUME = {154},
          URL = {http://dx.doi.org/10.1007/978-1-4614-1927-3_6},
         NOTE = {10.1007/978-1-4614-1927-3_6},
         YEAR = {2012},
  }
  

• Active-Set Methods for Quadratic Programming.
  Ph.D. Thesis, Department of Mathematics, University of California, San Diego (June 2011).
  ( bibtex | pdf )

  @phdthesis{Wong11,
       AUTHOR = {Elizabeth Wong},
       SCHOOL = {Department of Mathematics,
                 University of California, San Diego},
        TITLE = {Active-Set Methods for Quadratic Programming},
        MONTH = {June},
         YEAR = {2011}
  }
  

• H. D. I. Abarbanel, P. Bryant, P. E. Gill, M. Kostuk, J. Rofeh, Z. Singer, B. Toth, and E. Wong.
  Dynamical parameter and state estimation in neuron models.
  in M. Ding and D. Glanzman (eds), An Exploration of Neuronal Variability and its Functional Significance,
  Oxford University Press, Oxford and New York, 139--180, 2011.
  ( bibtex )

  @incollection{AbaBGKRSTW11,
       AUTHOR = {Abarbanel, Henry D. I. and  Bryant, Paul and  Gill, Philip E. and
                 Kostuk, Mark  and  Rofeh, Justin  and Singer, Zakary
                 and Toth, Bryan and Wong, Elizabeth},
        TITLE = {Dynamical parameter and state estimation in neuron models},
       EDITOR = {Ding, Mingzhou and Glanzman, Dennis},
    BOOKTITLE = {An Exploration of Neuronal Variability and its Functional Significance},
    PUBLISHER = {Oxford University Press},
      ADDRESS = {New York and Oxford},
        PAGES = {139--180},
         ISBN = {978-0-19-539379-8},
         YEAR = {2011},
  }
  

technical reports

• with Philip E. Gill. Methods for Convex and General Quadratic Programming.
  Report NA 10-1, Department of Mathematics, University of California, San Diego.
  ( abstract | bibtex | pdf )
  Computational methods are considered for finding a point that satisfies the second-order necessary conditions for a general (possibly nonconvex) quadratic program (QP). The first part of the paper defines a framework for the formulation and analysis of feasible-point active-set methods for QP. This framework defines a class of methods in which a primal-dual search pair is the solution of an equality-constrained subproblem involving a "working set" of linearly independent constraints. This framework is discussed in the context of two broad classes of active-set method for quadratic programming: binding-direction methods and nonbinding-direction methods. We recast a binding-direction method for general QP first proposed by Fletcher, and subsequently modified by Gould, as a nonbinding-direction method. This reformulation gives the primal-dual search pair as the solution of a KKT-system formed from the QP Hessian and the working-set constraint gradients. It is shown that, under certain circumstances, the solution of this KKT-system may be updated using a simple recurrence relation, thereby giving a significant reduction in the number of KKT systems that need to be solved.
  
  In the second part of the paper, the nonbinding-direction framework is applied to QP problems with constraints in standard form, and to the dual of a convex QP. Two approaches are considered for solving the constituent KKT systems. The first approach uses a variable-reduction technique requiring the calculation of the Cholesky factor of the reduced Hessian. The second approach uses a symmetric indefinite factorization of a fixed KKT matrix in conjunction with the factorization of a smaller matrix that is updated at each iteration. Finally, a linearly constrained augmented Lagrangian method is proposed that obviates the need for a separate procedure for finding a feasible point.

  @techreport{GilW10,
       AUTHOR = {Philip E. Gill and Elizabeth Wong},
        TITLE = {Methods for Convex and General Quadratic Programming},
  INSTITUTION = {Department of Mathematics, University of California, San Diego},
      ADDRESS = {La Jolla, CA},
         TYPE = {Numerical Analysis Report},
       NUMBER = {10-1},
         YEAR = {2010},
  }
  

software

• icQP :: a general QP solver
• SNCTRL5 :: an optimal control interface for SNOPT (updated: Feb 14, 2010) ( pdf documentation )

invited talks

• Active-set methods for large-scale quadratic programming
  Optimization 2011, Portugal, July 2011
• A regularized method for general quadratic programming
  Linear Algebra and Optimization Seminar, Stanford University, October 2009