mwang@watmath.UUCP (mwang) (10/18/83)
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- Friday, October 21, 1983.
Dr. R.H. Byrd of the University of Colorado at Boulder
will speak on ``Approximating the Projected Hessian in
Nonlinearly Constrained Optimization.''
TIME: 3:30 PM
ROOM: MC 5158
ABSTRACT
The most efficient algorithms for minimizing nonlinear
objective functions subject to nonlinear constraints
make use of the Hessian of the Lagrangian function.
Moreover, for a number of these methods, it is possible
to make use of only the projection of the Hessian onto
the null space of the active constraints. In this case
the theory suggests that a degradation in the rate of
convergence can happen if only the projection is used;
a degradation which is not evident in practice.
In this talk we will discuss the state of the art in
algorithms for the nonlinearly constrained optimization
problem and indicate why the projected Hessian plays
such an important role. An example will be shown exhi-
biting the expected degradation in convergence rate.
However, it will be shown that this degradation is a
result of looking at the iterates out of phase, and no
real loss of efficiency occurs. We will also show that
this phenomenon has a dual parallel in the well-known
method of multipliers for constrained optimization.
October 18, 1983