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.

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, box-bounded global optimization, global mixed-integer nonlinear programming, and exponential sum model fitting.

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...

TOMLAB is a general purpose, open and integrated Matlab development environment for research and teaching in optimization on Unix and PC systems. One motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having full access to the power of Matlab. The design principle is: define your problem once, optimize using any suitable solver. In this paper we discuss the design and contents of TOMLAB, as well as some applications where TOMLAB has been successfully applied. TOMLAB is based on NLPLIB TB, a Matlab toolbox for nonlinear programming and parameter estimation, and OPERA TB 1.0, a Matlab toolbox for linear and discrete optimization. More than 65 different algorithms and graphical utilities are implemented. It is possible to call solvers in the Matlab Optimization Toolbox and general-purpose solvers implemented in Fortran or C using a MEX-file interface. Currently, MEX-file interfaces have been developed for

Contents 1 The TOMLAB OpBP-yD-fP0 Environment 7 1.1 Backgrou nd................................................. 8 1.2 TheDesignofTOMLAB.......................................... 8 1.2.1 Global Variables . . ........................................ 22 1.3 SolverRou tinesinTOMLAB ....................................... 24 1.4 Menu ProgramsinTOMLAB....................................... 26 1.5 LowLevelRou tinesandTestProblems.................................. 27 1.5.1 Utility Test RouNEFF ........................................ 34 1.6 TheGraphicalUserInterface ....................................... 34 1.6.1 The Advanced Mode ........................................ 35 2 Solving Linear, Quadratic and Integer Programming Problems 39 2.1 Linear Programming Problems ...................................... 39 2.1.1 AQu0 k Linear Programming SoluxFz .............................. 39 2.1.2 Several Linear Programs ..................................... 39 2.1.

. In this paper algorithms for fitting exponential sums D (r) = P p i=1 a i (1 \Gamma exp (\Gammab i r)) to numerical data are presented and compared for efficiency and robustness. Estimating parameters in exponential sums is known as a classical and difficult problem, and here the numerical examples stem from parameter estimation in dose calculation for radiotherapy planning. The doses are simulated by emitting an ionizing photon beam into water and at different depths and different radius from the beam center measuring the absorption. The absorped dose is normally distinguished into primary dose from particles excited by the photon beam and scattered dose from the following particle interactions. The examined algorithms use interpolation methods to find initial approximations and then refine the parameters with modern iterative nonlinear least squares algorithms such as hybrid methods and structured secant methods. Hybrid methods switch between Gauss-Newton and a quasi-Newton metho...

In this paper we will discuss the efficiency and implementation details of an algorithm for finding the global minimum of a multivariate function subject to simple bounds on the variables. The algorithm, DIRECT, developed by D. R. Jones, C. D. Perttunen and B. E. Stuckman is a modification of the standard Lipschitzian approach that eliminates the need to specify a Lipschitz constant. We have implemented the DIRECT algorithm in Matlab and the efficiency of our implementation is analyzed by comparing it to the result of Jones's implementation on nine standard test problems for global optimization. In fifteen out of eighteen runs the results is to the favor of our implementation. For some test problems the differences in the number of function evaluations needed for the algorithm to converge are small but for others the differences are great enough to be worth a discussion. Our code is integrated in the NLPLIB TB Toolbox as part of the optimization environment TOMLAB. All tests are perfor...

TOMLAB is a Matlab 5 development environment for research and teaching in optimization, running on both Unix and PCsystems. One motivation for TOMLAB is to simplify research on practical optimization problems, giving easy access to all types of solvers; at the same time having full access to the power of Matlab. In this paper we discuss the design and contents of TOMLAB, as well as some applications where TOMLAB has been successfully applied. TOMLAB includes routines for linear, integer and nonlinear programming, nonlinear parameter estimation and global optimization. More than 65 algorithms are implemented, together with graphical and computational utilities, menu systems and a graphical user interface. It is possible to call solvers in the Math Works Optimization Toolbox and, using MEX-file interfaces, general-purpose solvers implemented in Fortran or C. TOMLAB implements powerful and robust state-of-the-art routines for nonlinear parameter estimation and global optimization; areas of special interest in applied research. Results on practical applications in these areas will be discussed. Our new algorithms for constrained nonlinear least squares algorithms are out-performing the state-of-the-art commercial solvers on classical test problems. For exponential sum model fitting on real-life data from radiotherapy planning our new separable nonlinear least squares algorithm is converging> 35 % faster than other solvers. 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