


NPSOL
5.0  Description 


NPSOL
(invented by Philip Gill, Walter
Murray, Michael Saunders and
Margaret Wright) is a software
package for solving constrained
optimization problems (nonlinear
programs). It employs a dense
SQP algorithm and is especially
effective for nonlinear problems
whose functions and gradients
are expensive to evaluate. The
functions should be smooth but
need not be convex. An augmented
Lagrangian merit function ensures
convergence from an arbitrary
point.










NPSOL
is designed to minimize
an arbitrary smooth function
subject to constraints, which
may include simple bounds
on the variables, linear constraints
and smooth nonlinear constraints.
(NPSOL may also be used for
unconstrained, boundconstrained
and linearly constrained optimization.)
The
user must provide subroutines
that define the objective
and nonlinear constraint functions
and (optionally) their gradients.
NPSOL uses dense matrix methods
and is intended for problems
with up to a few hundred constraints
and variables, depending on
the amount of memory available.








If the
functions or gradients
are expensive
to evaluate, NPSOL will
usually be more efficient
than MINOS.
NPSOL may be more reliable
on highly nonlinear
problems. It, like SNOPT,
uses an SQP algorithm
in which the sub problems
have the same linearized
constraints as in MINOS,
but the objective is
a quadratic approximation
to the Lagrangian. (Hence,
no function or gradient
values are needed during
the solution of each
QP.)










A merit function promotes
convergence from arbitrary
starting points.
NPSOL
contains a complete
and accessible version
of LSSOL,
a package for solving
linear and quadratic
problems and least square
problems with linear
constraints.












