Introduction to NLPQL solution process

1 Introduction

1.1 Overview

Welcome to the TOMLAB /NLPQL User's Guide. TOMLAB /NLPQL includes the NLPQLP, NLPJOB and DFNLP solvers from Klaus Schittkowski and an interface to The MathWorks' MATLAB.

TOMLAB /NLPQL solves general nonlinear mathematical programming problems with equality and inequality constraints. It is assumed that all problem functions are continuously differentiable.

The internal algorithm is a sequential quadratic programming (SQP) method. Proceeding from a quadratic approximation of the Lagrangian function and a linearization of the constraints, a quadratic subproblem is formulated and solved by dual code. Subsequently a line search is performed with respect to two alternative merit functions and the Hessian approximation is updated by the modified BFGS-formula.

TOMLAB /NLPJOB solves multicriteria optimization problems. NLPJOB offers a total of 15 different possibilities to transform the objective function vector into a scalar function. An SQP method is also used to solve the problem in this case.

TOMLAB /DFNLP is a sequential quadratic programming method for solving nonlinear data fitting problems. The algorithm introduces new decision variables as well as constraints to formulate a smooth nonlinear programming problem, which is solved by SQP.

1.2 Contents of this Manual

Section 1 provides a basic overview of the TOMLAB /NLPQL solver package.
Section 2 provides an overview of the Matlab interface to NLPQL.
Section 3 describes how to set NLPQL solver options from Matlab.
Section 4 gives detailed information about the interface routine nlpqlTL.
Section 5 gives detailed information about the interface routine nlpjobTL.
Section 6 gives detailed information about the interface routine dfnlpTL.

1.3 More information

Please visit the following links for more information:

1.4 Prerequisites

In this manual we assume that the user is familiar with global optimization and nonlinear programming, setting up problems in TOMLAB (in particular constrained nonlinear (con) problems) and the Matlab language in general.

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