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The TOMLAB Graphical User Interface for Nonlinear Programming. Advanced Modeling and Optimization
 in MATLAB. Annals of Operations Research, Modeling Languages and Approaches: Submitted
, 1999
"... 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 LIBrary Toolbox) � a set of Matlab solvers, test problems, graphical and computational utilities for unconstrained and constrain ..."
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Cited by 14 (9 self)
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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 LIBrary 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, boxbounded global optimization, global mixedinteger 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 amultisolver 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 standalone 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 TOMLAB OPERA Toolbox for Linear and Discrete Optimization. Advanced Modeling and Optimization
, 1999
"... 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). ..."
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Cited by 9 (8 self)
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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, generalpurpose 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 primaldual interiorpointLP solver in the same toolbox. Running the commercial Fortran solvers using MEX le interfaces gives a speedup factor of ve to thirty ve.
Constrained Separable NLLS Algorithms for Chemical Equilibrium Analysis
 DIVISION OF OPERATIONS RESEARCH, MOLDE UNIVERSITY
, 1998
"... We present new algorithms for constrained separable nonlinear least squares (NLLS) problems. The algorithms are used to determine models and parameters in multiphase inorganic equilibria using multimethod data. The algorithms are implemented in the Matlab toolbox LAKE TB and is part of our program ..."
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Cited by 6 (3 self)
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We present new algorithms for constrained separable nonlinear least squares (NLLS) problems. The algorithms are used to determine models and parameters in multiphase inorganic equilibria using multimethod 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.
Initial Values for the Exponential Sum Least Squares Fitting Problem
, 1998
"... 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, go ..."
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Cited by 6 (4 self)
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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 onevariable 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...
Initial Values for a Class of Exponential Sum Least Squares Fitting Problems
, 1998
"... 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 ..."
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Cited by 5 (4 self)
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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 semiheuristic 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...
Identifying Parameters and Model Order for Two Classes of Exponential Sums
, 1998
"... 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 ..."
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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 MLmeasures 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...
Practical optimization with the tomlab environment in matlab
 IN PROC. 42ND SIMS CONF
, 2001
"... The TOMLAB /SOL v3.0 optimization environment is a powerful optimization tool in Matlab, which incooperates many results 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 Fortra ..."
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Cited by 1 (0 self)
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The TOMLAB /SOL v3.0 optimization environment is a powerful optimization tool in Matlab, which incooperates many results 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 at
Temperature modelling and Model Predictive Control of a pilotscale batch reaction system
, 2014
"... The temperature control equipment on a pilot scale batch reaction system located at EAFIT University in Medelĺın, Colombia, is modeled and a new controller is designed aiming at using it in the reactor current PLCbased control system. Some mathematical models are developed from experimental data t ..."
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The temperature control equipment on a pilot scale batch reaction system located at EAFIT University in Medelĺın, Colombia, is modeled and a new controller is designed aiming at using it in the reactor current PLCbased control system. Some mathematical models are developed from experimental data to describe the system behavior and using them several model based predictive controllers are designed. The simplest, yet reliable, model obtained is an ARX polynomial model of order (1,1,1) that yields a four states affine model for which an explicit MPC was calculated. This controller has a reduced mathematical complexity and can probably be used directly on the existing control system.
Methods for Parameter Estimation in Exponential Sums
 Molde University
, 1998
"... 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 ..."
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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 ...
Initial Values for Two Classes of Exponential Sum Least Squares Fitting Problems
, 1998
"... 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 hav ..."
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Cited by 1 (1 self)
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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...