PORT

General minimization, nonlinear least squares, separable nonlinear least squares, linear inequalities, linear programming, and quadratic programming.

The nonlinear optimizers have unconstrained and bound-constrained variants, and use trust region algorithms. Gradients and Jacobians can be provided by the caller or approximated automatically by finite differences. The general minimization routines use either a quasi-Newton approximation to the Hessian matrix or a Hessian provided by the caller; the nonlinear least squares routines adaptively switch between the Gauss-Newton Hessian approximation and an "augmented" approximation that uses a quasi-Newton update. Function and, if necessary, gradient values may be provided either by subroutines or by reverse communication.

There is a special separable nonlinear least squares solver for the case of one nonlinear variable; it uses Brent's one-dimensional minimization algorithm for the nonlinear variable. Brent's algorithm is also available by itself, as is an implementation of the Nelder-Mead simplex method.

The feasible point (linear inequalities) and linear and quadratic programming routines start by taking steps through the interior and end with an active set strategy. The quadratic programming solvers use the Bunch-Kaufman factorization and thus can find local minimizers of indefinite problems.

None of the solvers is meant for large numbers of variables. When there are n variables and m equations (where m = 1 for general minimization), the nonlinear solvers require O( n ^ 2 m ) or O( n ^ 3 ) arithmetic operations per iteration. The linear and quadratic solvers use dense-matrix techniques.

Software is written in ANSI Fortran 77, with single- and double-precision versions of all solvers. Machine-dependent constants are provided by subroutines I1MACH, R1MACH, and D1MACH.

Need more info?

Or contact the software distribution people at Lucent Technologies.

References:

J. E. Dennis, Jr., D. M. Gay, and R. E. Welsch, Algorithm 573. NL2SOL -- An adaptive nonlinear least-squares algorithm , ACM Trans. Math. Software 7 (1981), pp. 369-383.

P. A. Fox, A. D. Hall, and N. L. Schryer, The PORT mathematical subroutine library, ACM Trans. Math. Software 4 (1978), pp. 104-126.

D. M. Gay, , ACM Trans. Math. Software 9 (1983), pp. 503--524.

D. M. Gay, Usage summary for selected optimization routines, Computing Science Technical Report No. 153, AT\&T Bell Laboratories, Murray Hill, NJ, 1990. (Postscript for the last report is available by sending the message send 153 from research/cstr to netlib@research.att.com.)

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