Advanced Modeling and Optimization

Abstract for Paper 4 of Volume 1, Number 1, 1999, pp.70-86

The TOMLAB NLPLIB Toolbox for Nonlinear Programming


Kenneth Holmström and Mattias Björkman
Center for Mathematical Modeling,
Department of Mathematics and Physics
Mälardalen University, P.O. Box 883, SE­721 23 Västerås,
Sweden
Abstract

The paper presents the toolbox NLPLIB TB 1.0 (NonLinear Programming LIBrary); a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, box­bounded global optimization, global mixed­integer nonlinear programming, and exponential sum model fitting.

NLPLIB TB, like the toolbox OPERA TB for linear and discrete optimization, is a part of TOMLAB; an environment in Matlab for research and teaching in optimization. TOMLAB currently solves small and medium size dense problems.

Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Matlab Optimization Toolbox. MEX­file interfaces are prepared for seven Fortran and C solvers, and others are easily added using the same type of interface routines.

Currently, MEX­file interfaces have been developed for MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. There are four ways to solve a problem: by a direct call to the solver routine or a call to a multi­solver driver routine, or interactively, using the Graphical

User Interface (GUI) or a menu system. The GUI may also be used as a preprocessor to generate Matlab code for stand­alone runs. If analytical derivatives are not available, automatic differentiation is easy using an interface to ADMAT/ADMIT TB. Furthermore, five types of numerical differentiation methods are included in NLPLIB TB. NLPLIB TB implements a large set of standard test problems. Using MEX­file interfaces, problems in the CUTE test problem data base and problems defined in the AMPL modeling language can be solved.

TOMLAB and NLPLIB TB have been used to solve several applied optimization problems. New types of algorithms are implemented for the nonlinear least squares problem to approxi­ mate sums of exponential functions to empirical data and for global optimization. We present some preliminary test results, which show very good performance for the NLPLIB TB solvers.