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NLPLSX

Nonlinear Least Squares Optimization with Very Many Observations

Version 2.5 (2011)

## Purpose

NLPLSX solves constrained nonlinear least squares problems, i.e., nonlinear optimization problems, where the objective function is the sum of squares of function. In addition there may be any set of equality or inequality constraints. It is assumed that all individual problem functions are continuously differentiable, and that the number of squared functions or, alternatively, the number of experimental data is too large to apply an available Gauss-Newton-type algorithm.

## Numerical Method

The problem is transformed into a general smooth nonlinear programming problem which is then solved by the sequential quadratic programming (SQP) code NLPQLP.

## Program Organization

NLPLSX is a double precision FORTRAN subroutine and parameters are passed through arguments.

## Special Features

- reverse communication
- nonlinear constraints
- bounds and linear constraints remain satisfied
- FORTRAN source code (close to F77, conversion to C by f2c possible)

## Applications

NLPLSX is part of the interactive data fitting system EASY-FIT which contains now 1,300 test examples.

## Reference

- K. Schittkowski, NLPLSX: A Fortran implementation of an SQP-Gauss-Newton algorithm for least squares optimization with very many constraints, Report, Department of Computer Science, University of Bayreuth (2008)
- K. Schittkowski, NLPLSQ: A Fortran implementation of an SQP-Gauss-Newton algorithm for least squares optimization, Report, Department of Computer Science, University of Bayreuth (2007)
- K. Schittkowski, DFNLP: A Fortran implementation of an SQP-Gauss-Newton algorithm, Report, Department of Computer Science, University of Bayreuth (2005)
- K. Schittkowski (2002): EASY-FIT: A software system for data fitting in dynamic systems, Structural and Multidisciplinary Optimization, Vol. 23, No. 2, 153-169
- K. Schittkowski (2002): Numerical Data Fitting in Dynamical Systems - A Practical Introduction with Applications and Software, Kluwer Academic Publishers
- K. Schittkowski, Solving nonlinear least squares problems by a general purpose SQP-method, in: Trends in Mathematical Optimization, K.-H. Hoffmann, J.-B. Hiriart-Urruty, C. Lemarechal, J. Zowe eds., International Series of Numerical Mathematics, Vol. 84, Birkhaeuser, 1988