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 non-linear constraints. (NPSOL may also be used for unconstrained, bound-constrained 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.


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