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\title{Numerical Experiment for Large-Scale Optimization Problem}
\author{Li-Zhi Liao\\
Department of Mathematics, Hong Kong Baptist University}
\date{}
\maketitle
Large-scale optimization problems normally possess certain attractive 
structures.  It is a very challenging but rewarding task to recognize
these structures and explore them in optimization methods.  The
optimal control approach, which was proposed recently for large-scale
unconstrained optimization problems, provides some interesting ideas 
to absorb these structures and be able to solve these problems
efficiently and economically.

\vskip 2truemm

In this research, we will investigate and reported the numerical aspect
of the optimal control approach for some large-scale unconstrained optimization 
problems. Around 30 large-scale (problem size $\ge 10^6$) unconstrained 
optimization problems in the literature are selected.  The numerical results
of these problems by both the optimal control approach and a leading 
optimization software package {\em LANCELOT} will be reported.  These
numerical results clearly indicate the attractiveness of the optimal
control approach.


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