%%Please answer the following:
%%
%%1.  Name of conference  Applied Linear Algebra
%%2.  Type of Presentation  contributed talk
%%      Contributed:  Lecture form    YES
%%                    Poster form     
%%      Minisymposium:    
%%3.  Equipment for Visual Support
%%      Lecture Form/Minisymposium:
%%            Overhead Projector    
%%            2" x 2" Slide Projector (35mm)    
%%      Poster Form:
%%            Easel     Poster Board    
%%            Other (specify)           
%%
%%More sophisticated equipment can be provided, but you may be
%%required to pay the rental fee.  For details, indicate your 
%%requirements below:
%%
%%4.  If you are a speaker in a minisymposium, who is the organizer?
%%5.  What is the minisymposium title?
%%6.  If more than one author, who will present the paper?
%%7.  Please include at least 3 keywords but no 
%%    more than 5 in order of importance below.
%%            
%%
% This is a macro file for creating a SIAM Conference abstract in
% LaTeX.
%
% If you have any questions regarding these macros contact:
% For contributed:  Lillian Hunt, meetings@siam.org
% For minisymposia: Maryann M. Donaghy, donaghy@siam.org
%                   SIAM
%                   3600 University City Center Center
%                   Philadelphia, PA 19104-2688
%                   USA
%                   (215) 382-9800      

\hsize=25.5pc
\vsize=50pc
\textheight 50pc
\textwidth 25.5pc
\parskip 0pt
\parindent 0pt
\pagestyle{empty}

\def\title#1{\bf{#1}\vspace{8pt}}
\def\abstract#1{\rm {#1}\vspace{8pt}}
\def\author#1{\rm {#1}\vspace{2in.}}

% end of style file

% 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{Newton Directions and Least Squares for Semidefinite
Programming}
 
\abstract{Primal-dual 
interior-point methods have proven to be the solution method
of choice for semidefinite programming (SDP)
problems. Many of the techniques that have
been so successful for linear programming (LP)  have been extended to
SDP.
However, there is one major difference between LP and SDP that raises
several interesting questions. That difference is the form of the
complementarity condition used in the optimality conditions,
i.e. $ZX - \mu I = 0.$
The primal matrix $X$ and the dual slack matrix $Z$ are diagonal
in LP but may only be
symmetric in SDP; this results in $ZX$ not being symmetric in
general. In addition, problems with numerical instability can
arise near the optimal solution.\\
There have been various approaches which attempt to symmetrize
the complementarity condition so that the linearization of the
optimality
conditions are ``square'', i.e. map between the same spaces. We consider
different approaches which require no symmetrization.
We concentrate on solving the ``nonsquare,'' or overdetermined, system
using nonlinear least squares. In particular, we use
Gauss-Newton type methods.
}

%Please use command \underbar for the speaker only.   

\author{\underbar{Henry Wolkowicz}\\
University of Waterloo, Waterloo, Ont. Canada\\
\\
}

\end{document}

% end of example file.

%Please furnish complete addresses all co-authors.
%Henry Wolkowicz                |Fax:   (519) 725-5441
%University of Waterloo         |Tel:   (519) 888-4567, 1+ext. 5589
%Dept of Comb and Opt           |email:  henry@orion.math.uwaterloo.ca
%Waterloo, Ont. CANADA N2L 3G1  |URL: http://orion.math.uwaterloo.ca/~hwolkowi


%PLEASE INDICATE WHAT CONFERENCE ABSTRACT IS FOR.
%Applied Linear Algebra Oct 29/97 Snowbird Utah
