Nonlinear Least Squares Optimization

Version 4.0 (2013)


NLPLSQ 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.

Numerical Method

By introducing additional variables and constraints, the problem is transformed into a general smooth nonlinear programming problem which is then solved by the sequential quadratic programming (SQP) code NLPQLP. It can be shown that typical features of special purpose algorithms are retained, i.e., a combination of a Gauss-Newton and a quasi-Newton search direction. The additionally introduced variables are eliminated in the quadratic programming subproblem, so that calculation time is not increased significantly.

Program Organization

NLPLSQ 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)


In its previous version (DFNLP), the code is in practical use to solve parameter estimation problems, e.g., in chemical and pharmaceutical applications. Customers include BASF, Battery Design, Bayer, Boehringer Ingelheim, Dow Chemical, GLM Lasertechnik, Envirogain, Epcos, Eurocopter, Institutt for Energiteknikk, Novartis, Oxeno, Prema, Prodisc, Springborn Laboratories, and dozens of academic research institutions worldwide. Moreover, NLPLSQ is part of the interactive data fitting system EASY-FIT which contains now 1,300 test examples.