The paper presents a Graphical User Interface (GUI) for nonlinear programming in Matlab. The GUI gives easy access to all features in the NLPLIB TB (NonLinear Programming LI-Brary Toolbox) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrained optimization, quadratic programming, unconstrained and constrained nonlinear least squares, box-bounded global optimization, global mixed-integer nonlinear programming, and exponential sum model tting. The GUI also runs the linear programming problems in the linear and discrete optimization toolbox OPERA TB. Both NLPLIB TB and OPERA TB are part of TOMLAB � an environment in Matlab for research and teaching in optimization. Presently, NLPLIB TB implements more than 25 solver algorithms, and it is possible to call solvers in the Math Works Optimization Toolbox. MEX- le interfaces are developed for seven Fortran and C solvers, and others are easily added using the same type of interface routines. There are four ways to solve a problem: by a direct call to the solver routine or a call to amulti-solver driver routine, or interactively, using the Graphical User Interface or a menu system. The GUI may alsobe used as a preprocessor to generate Matlab code for stand-alone runs. Alargeset of standard test problems is implemented in TOMLAB. Furthermore, using MEX- le interfaces, problems in the CUTE test problem data base and problems de ned in the AMPL modeling language can be solved.

The Matlab toolbox OPERA TB is a set of Matlab m- les, which solves basic linear and discrete optimization problems in operations research and mathematical programming. Included are routines for linear programming (LP), network programming (NP), integer programming (IP) and dynamic programming (DP). OPERA TB, like the nonlinear programming toolbox NLPLIB TB, is a part of TOMLAB � an environment in Matlab for research and teaching in optimization. Linear programs are solved either by direct call to a solver routine or to a multisolver driver routine, or interactively, using the Graphical User Interface (GUI) or a menu system. From OPERA TB it is possible to call solvers in the Math Works Optimization Toolbox and, using a MEX- le interface, general-purpose solvers implemented in Fortran or C. The focus is on dense problems, but sparse linear programs may be solved using the commercial solver MINOS. Presently, OPERA TB implements about thirty algorithms and includes a set of test examples and demonstration les. This paper gives an overview of OPERA TB and presents test results for medium size LP problems. The tests show that the OPERA TB solver converges as fast as commercial Fortran solvers and is at least ve times faster than the simplex LP solver in the Optimization Toolbox 2.0andtwice as fast as the primal-dual interior-pointLP solver in the same toolbox. Running the commercial Fortran solvers using MEX- le interfaces gives a speed-up factor of ve to thirty- ve.

We present new algorithms for constrained separable nonlinear least squares (NLLS) problems. The algorithms are used to determine models and parameters in multi-phase inorganic equilibria using multi-method data. The algorithms are implemented in the Matlab toolbox LAKE TB and is part of our program package LAKE. LAKE has for more than ten years been used for equilibrium analysis by inorganic researchers. 2 The TOM home page is http://www.ima.mdh.se/tom. Constrained Separable NLLS Algorithms for Chemical Equilibrium Analysis 2 1 Introduction The chemical equilibrium problem is a well-known and much studied practical optimization and modeling problem. In inorganic chemistry solution chemistry research groups work on solving these type of problems on a daily routine basis. Development of advanced computer software started already around 1960 and the program LETAGROP [22] was one of the first attempts. Since 1983 we have been working with the development of algorithms and software for...

In an earlier report the authors developed an initial value algorithm for one class of exponential sum least squares fitting problems. As a natural extension of that problem the authors in this paper develop an initial value algorithm for a slightly different model in the class of exponential models, f (t) = P p i=1 a i (1 \Gamma exp (\Gammab i t)), which occurs in radiophysics in medicin. A method of generalized interpolation will provide initial values a = [a 1 ; :::; a p ] ; b = [b 1 ; :::; b p ] and these are refined by iterative least squares algorithms. New initial value algorithms are developed. For data equidistant in time, generalized interpolation gives explicit expressions for p 2 and a semi-heuristic solution for p 3. For data not equidistant in time, the numerical derivatives are estimated. The derivative is another exponential sum for which the authors earlier have developed an initial value algorithm for arbitrary number of terms and data not equidistant in time...

Exponential sum models f (t) = P p i=1 a i exp (\Gammab i t) are used frequently: In heat diffusion, diffusion of chemical compounds, time series in medicine, economics and the physical sciences and technology. As the fitting of an exponential sum by e.g. a least squares criterion is difficult, good initial values for the parameters a = [a 1 ; :::; a p ] ; b = [b 1 ; :::; b p ] are needed. Interpolation methods will provide initial values and these are then refined by general least squares algorithms. New initial value algorithms are developed. For data equidistant in time, generalized interpolation gives explicit expressions for p 2, and a numerically solvable one-variable equation for 3 p 4. For p ? 4 we use a heuristic algorithm to get rough initial values. For data not equidistant in time a two point interpolation by a exp (\Gammabt) will generate artificial data points equidistant in time. The least squares refinement is not using the artificial data. Numerical results are p...

In two earlier papers, the authors developed initial value algorithms for the two classes of least squares fitting of exponential sums P p i=1 a i exp (\Gammab i t) and P p i=1 a i (1 \Gamma exp (\Gammab i t)). In some cases one does not know the model order a priori, and as these problems are strongly nonlinear in the exponentials and close to linear dependent in the linear coefficients, it is of interest to have a theoretical argument for how many terms that are needed to fit data well. For this we investigate the minizing of some information criteria depending on different penalties for the model order, namely minimizing prediction error and shortest description of data, and the two ML-measures for normal- and Cauchy distributions of distance between data and the estimated exponential sum. The conclusion is that the first exponential sum is not sensitive to the choice of information criterion while the second exponential sum is. A recommendation is to try several c...

The authors have earlier developed new initial value algorithms to least squares fitting of two classes of exponential sum models by generalized interpolation (GI). In this report the class f (t) = P p i=1 (a i t + c i ) exp (\Gammab i t) and its subclass, when all c i = 0, are treated. They have application in statistical physics. Initial values for a = [a 1 ; :::; a p ]; b = [b 1 ; :::; b p ] and c = [c 1 ; :::; c p ] are given by an explicit formula when p = 1 and a one dimensional root search algorithm when p = 2. A new numerical analogy, generalized Prony method (GP), is derived. Numerical results are reported. 1 Introduction In for example statistical physics sometimes the question of fitting functions f (t) = p X i=1 a i t exp (\Gammab i t) (1) 1 The TOM home page is http://www.ima.mdh.se/tom. 1 2 to data appear. This function is generalized version of the gamma distribution P p i=1 ff i \Gamma(2; b i ). A similar function is f (t) = p X i=1 (a i t + c i ) ex...

In this paper we discuss the problem of fitting the exponential model f (t) = P p i=1 a i exp (\Gammab i t) to empirical data y (t j ) ; j = 1; ::; m. The number of terms p is determined by an information criterion and the parameters a = [a 1 ; :::; a p ] and b = [b 1 ; :::; b p ] are determined by a least squares criterion. An algorithm is developed which finds initial values when p 4 for the nonlinear parameter estimation problem. Test results are presented. 1 Introduction In this paper we discuss the problem of fitting f (t) = P p i=1 a i exp (\Gammab i t) to empirical data y (t j ) ; j = 1; ::; m. The number of terms p is determined by an information criterion and the parameters a = [a 1 ; :::; a p ] and b = [b 1 ; :::; b p ] are estimated by minimizing a least squares criterion. Depending on the starting values used a nonlinear least squares algorithm may fail to converge. We have developed an algorithm to find initial values of the parameters, to help the convergence. 1 ...

The TOMLAB /SOL v3.0 optimization environment is a powerful optimization tool in Matlab, which incooperates manyresults from the last 40 years of research in the field. More than 65 different algorithms for linear, discrete, global and nonlinear optimization are implemented in Matlab, and 14 Fortran solvers are integrated with the use of MEX file interfaces. It has been developed in cooperation with the SOL group

this paper we discuss the design and contents of TOMLAB. TOMLAB