User's Guide for NPSOL (Version 4.0): A Fortran Package for Nonlinear Programming.
STANFORD UNIV CA SYSTEMS OPTIMIZATION LAB
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This report forms the users guide for Version 4.0 of NPSOL, a set of Fortran subroutines designed to minimize a 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, bound-constrained and linearly constrained optimization. The user must provide subroutines that define the objective and constraint functions and optionally their gradients. All matrices are treated as dense, and hence NPSOL is not intended for large sparse problems. NPSOL uses a sequential quadratic programming SQP algorithm, in which the search directions is the solution of a quadratic programming QP subproblem. The algorithm treats bounds, linear constraints and nonlinear constraints separately. The Hessian of each QP subproblem is a positive-definite quasi-Newton approximation to the Hessian of the Lagrangian function. The steplength at each iteration is required to produce a sufficient decrease an augmented Lagrangian merit function. Each QP subproblem is solved using a quadratic programming package with several features that improve the efficiency of an SQP algorithm. Author
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