User's Guide for NPSOL (version 4.0): a Fortran Package for Nonlinear ProgrammingStanford University, Department of Operations Research, Systems Optimization Laboratory, 1986 - Mathematical optimization - 54 pages This report forms the user's 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). |
Common terms and phrases
algorithm array of dimension BIGBND BL(j bounds and linear BU(j CALL NPOPTN call to NPSOL Cholesky factor CJAC CLAMDA components computed CONFN2 constraint gradients default value defined Derivative Level dimension at least DOUBLE PRECISION Euclidean norm F FF feasible point Fortran Gill inequality constraint INFORM initial working set Input INTEGER ISTATE Jacobian elements Jacobian matrix Lagrange multipliers Lagrangian Lagrangian merit function LENW linear constraints Linear Feasibility Tolerance linesearch lower bound LSSOL Major Iteration Limit Major Print Level MCHPAR minor iteration NCLIN NCNLN NEEDC NLCON Nolist nonlinear constraints Nonlinear Feasibility Tolerance Nonlinear Programming Norm Gz NPFILE NPSOL NROWA NROWJ NROWR NSTATE objective function objective gradient OBJF OBJFN1 OBJGRD Optimality Tolerance optional parameter options file predicted active set problem projected gradient QP subproblem quadratic programming real array search direction Section 5.2 sequential quadratic programming solution source files specified subroutines subroutines OBJFUN upper bound vector Verify Level Warm Start zero