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%Please answer the following:
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%1.  Name of conference  Fifth SIAM Conference on Optimization
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%2.  Type of Presentation
%      Contributed:  Lecture form    
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%3.  Equipment for Visual Support
%            Overhead Projector    
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%6.  If more than one author, who will present the paper?
%            Serge Kruk
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%7.  Please list at least 3 but no more than 5 keywords below
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% Nonlinear Programming, Sequential Quadratic Programming, Semidefinite programming
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% This is ltexconf.tex. Use this file as an example file for doing an SIAM
% Conference abstract in LaTeX.
   

\documentstyle[ltexconf]{report} 
\begin{document}
 
\title{S$\mbox{Q}^2$P via SDP for NLP }
 
\abstract{
One of the most popular and successful family of
methods for nonlinear programming (NLP) is the sequential quadratic
programming (SQP) approach. At a current
iterate, the NLP is approximated by a quadratic
programming model (QP) i.e.
a subproblem is solved which consists of an objective
function based on a quadratic approximation of the Lagrangian
and constraints formed from linear approximations of the NLP
constraints.
Using linear approximations for the constraints is compensated for by
using the Hessian of the Lagrangian in the objective function.
The linearly constrained
subproblem yields an update for the Lagrange multipliers as well as
a search direction. The search direction and a merit function are used
to find an update to the current approximation of the optimum.\\
We introduce the sequential quadratically constrained quadratic
programming
(S$\mbox{Q}^2$P) method.
This technique uses a quadratically constrained quadratic (Q$^2$P)
program for the subproblem.
A semidefinite programming (SDP) relaxation of Q$^2$P
is used to find an update to the Lagrange
multipliers. Thus it uses current curvature information of the
constraints.
This is a better subproblem since it uses quadratic approximations of
the
constraints and thus allows greater flexibility in choosing the
Lagrange multiplier updates from the
curvature information of the constraints.
}   

\author{\underbar{     Serge Kruk,
  Gabor Pataki,
          Henry Wolkowicz,
 Qing Zhao}\\
 University of Waterloo, Waterloo, Ontario \\
}

\eject 

\end{document}

% end of example file.


Please furnish complete addresses all co-authors.

 Department of Combinatorics and Optimization
 University of Waterloo, Waterloo, Ontario 
  Canada, N2L 3G1

PLEASE INDICATE WHAT CONFERENCE ABSTRACT IS FOR.
%1.  Name of conference  Fifth SIAM Conference on Optimization


