NLSSOL

Minimization of a sum of squares of smooth nonlinear functions subject to a set of constraints on the variables.

NLSSOL is a Fortran package designed to solve the constrained nonlinear least squares problem: the minimization of a sum of squares of smooth nonlinear functions subject to a set of constraints on the variables. The problem is assumed to be stated in the following form:

where the f_i(x) are nonlinear functions, the y_i are constant, A is an n_l x n matrix, and c(x) is an m_N-vector of nonlinear constraints.

The user must supply an initial estimate of the solution of the problem, subroutines that evaluate f(x), c(x), and as many first partial derivatives as possible; unspecified derivatives are approximated by finite differences.

NLSSOL is a sequential quadratic programming (SQP) method incorporating an augmented Lagrangian merit function and a BFGS quasi-Newton approximation to the Hessian of the Lagrangian. Features of NLSSOL include the explicit use of the Jacobian of f(x) and the ability to define an initial approximate Hessian suitable for least squares problems.

NLSSOL utilizes subroutines from the NPSOL and LSSOL packages, which are distributed together with NLSSOL.

NLSSOL contains approximately 16,500 lines of Fortran, of which about 75% are comments. The source code and example program for NLSSOL are distributed on a floppy disk. The code is also available via Internet using ftp.

NLSSOL includes calls to both Level-1 (vector) and Level-2 (matrix-vector) Basic Linear Algebra Subroutines (BLAS). They may be replaced by versions of the BLAS routines that have been tuned to a particular machine.

NLSSOL is written in ANSI Fortran 77 and should run without alteration on any machine with a Fortran 77 compiler. The code was developed on a DECstation 3100 using the MIPS f77 compiler and has been installed on most types of PC, workstation, and mainframe.

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 Prof. Walter Murray                   Prof. Philip E. Gill
 Department of Operations Research     Department of Mathematics 
 Terman Engineering Center             University of California, San Diego
 Stanford University	               9500 Gilman Drive               
 Stanford, CA 94305-4022               La Jolla, CA 92093-0112 
 

Reference:

P.E. Gill, W. Murray, M.A. Saunders, and M.H. Wright, Some theoretical properties of an augmented Lagrangian merit function, in Advances in Optimization and Parallel Computing, P.M. Pardalos, ed., North Holland, 1992, pp. 101--128.

P.E. Gill, W. Murray, M.A. Saunders, and M.H. Wright, User's Guide for NPSOL (Version 4.0): A Fortran package for nonlinear programming, SOL 86-2, 1986.

NAG Fortran Library Manual, Mark 15, NAG Ltd., 1991.

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