DFNLP

Constrained least squares, L1, and min-max optimization

DFNLP solves constrained nonlinear least squares, L1- and min-max problems, where the objective function is of the form

• sum of squares of function values,
• sum of absolute function values,
• maximum of absolute function values,
• maximum of functions.

In addition there may be any set of equality or inequality constraints. It is assumed that all individual problem functions are continuously differentiable.

By introducing additional variables and constraints, the problem is transformed into a general smooth nonlinear programming problem which is then solved by NLPQL. For least squares problems 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. In this case, the additionally introduced variables are eliminated in the quadratic programming subproblem, so that calculation time is not increased significantly.

Special features of DFNLP are

• reverse communication;
• bounds and linear constraints remain satisfied;
• internal scaling;
• FORTRAN source code;
• full documentation by initial comments.

DFNLP is a double precision FORTRAN-77 subroutine and parameters are passed through arguments.

Need more info?

Take a look at the author's home page, or contact

Prof. K. Schittkowski 
Dept. of Mathematics
University of Bayreuth 
95440 Bayreuth, Germany 

klaus.schittkowski@uni-bayreuth.de

Reference:

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.

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