## TOMLAB -- An Environment for Solving Optimization Problems in MATLAB (1997)

Venue: | PROCEEDINGS FOR THE NORDIC MATLAB CONFERENCE '97 |

Citations: | 14 - 12 self |

### BibTeX

@INPROCEEDINGS{Holmström97tomlab--,

author = {Kenneth Holmström},

title = {TOMLAB -- An Environment for Solving Optimization Problems in MATLAB},

booktitle = {PROCEEDINGS FOR THE NORDIC MATLAB CONFERENCE '97},

year = {1997},

pages = {27--28},

publisher = {}

}

### OpenURL

### Abstract

TOMLAB is a general purpose, open and integrated MATLAB environment for solving optimization problems on UNIX and PC systems. TOMLAB has meny systems and driver routines for the most common optimization problems and more than 50 algorithms implemented in the toolbox NLPLIB and the toolbox OPERA. NLPLIB TB 1.0 is a MATLAB toolbox for nonlinear programming and parameter estimation and OPERA TB 1.0 is a MATLAB toolbox for operational research, with emphasis on linear and discrete optimization. Of special interest in NLPLIB TB 1.0 are the algorithms for general and separable nonlinear least squares parameter estimation. TOMLAB is using MEX-file interfaces to call solvers written in C/C++ and FORTRAN. Currently MEXfile interfaces have been developed for the commercial solvers MINOS, NPSOL, NPOPT, NLSSOL, LPOPT, QPOPT and LSSOL. From TOMLAB it is also possible to call routines in the MathWorks Optimization Toolbox. Interfaces are available for the model language AMPL and the CUTE (Cons...

### Citations

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1352 |
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Citation Context ... squares is discussed in more detail in the next section 4.1. 4 The prototype routine for unconstrained optimizationscalled ucsolve handles problems with bound constraints as described in Gill et al. =-=[16]-=-. This routine implements the Newtons method, the Quasi Newton BFGS method, the inverse BFGS, the Fletcher-Reeves conjugate gradient method and the Polak-Ribiere conjugate gradient method. Included is... |

1082 |
Practical Methods of Optimization
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Citation Context ...ith a null space method (qpe) or with Lagranges method (qplm). The line search algorithm linesrch used by the solvers in NLPLIB (consolve, gn, ucsolve) is a modified version the algorithm in Fletcher =-=[12]-=-. Quadratic (intpol2) or cubic interpolation (intpol3) is possible in the line search -1-0.5 0 0.5 1 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 Rosenbrocks banana Figure 2: Search path of Fletcher-Reeves conjugate ... |

1045 |
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Citation Context ...r constraints a sequential quadratic programming (SQP) method by Schittkowski [30] is implemented in routine consolve. Quadratic programming (QP) problems are solved with a standard active set method =-=[25]-=-, routine qpi. In NLPLIB there are also two routines for solving QP with equality constraints, either with a null space method (qpe) or with Lagranges method (qplm). The line search algorithm linesrch... |

533 | Network flows - Ahuja, Magnanti, et al. - 1993 |

255 | A Users Guide
- Brooke, Kendrick, et al.
- 1998
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Citation Context ...uted by using numerical differences or nowadays using automatic differentiation techniques. In recent years several modeling languages has been developed, like AIMMS [6], AMPL [14], ASCEND [27], GAMS =-=[7, 9]-=- and LINGO [1]. The modeling system acts as a preprocessor. The user describes his problem in detail in a very verbal language, an opposite to a concise mathematical description of the problem. This p... |

176 | Linear Programming and Network Flows - Bazaraa, Jarvis, et al. - 1990 |

123 |
CUTEr, a Constrained and Unconstrained Test Environment, revisited. http://cuter.rl.ac.uk/cuter-www
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Citation Context ...d optimization software. Works for both PC and UNIX. Currently MINOS, NPSOL, NPOPT, NLSSOL, QPOPT, LSSOL and LPOPT. ffl TOMLAB interface to the CUTE SIF language and the standard set of test problems =-=[8]-=-. The CUTE distribution includes MATLAB interface routines. ffl TOMLAB interface to the AMPL model language[14]. The MATLAB Interface to AMPL was built by Gay [15]. ffl Integrated possibility to call ... |

118 |
The traveling-salesman problem and minimum spanning trees
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Citation Context ...n Ahuja et al. [3, page 415]. ffl Solve the symmetric travelling salesman problem using Lagrangian relaxation and the sub gradient method with Polyak rule II (salesman), an algorithm by Held and Karp =-=[19]-=-. Two algorithmic examples of dynamic programming are included. Both algorithms are described in Winston [32, chap. 20]. Forward recursion is used to solve an inventory problem (dpinvent) and a knapsa... |

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Citation Context ...ariables x. The problem is solved by relaxing all but one constraint and hence solving simple knapsack problems as subproblems in each iteration. The algorithm is based on the presentation in Fischer =-=[11]-=-, using subgradient iterations and a simple line search rule. 4 The NLPLIB Toolbox The current status of the NLPLIB toolbox is: ffl 15 400 lines of MATLAB code. ffl 101 files with algorithms, utilitie... |

63 |
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Citation Context ...uted by using numerical differences or nowadays using automatic differentiation techniques. In recent years several modeling languages has been developed, like AIMMS [6], AMPL [14], ASCEND [27], GAMS =-=[7, 9]-=- and LINGO [1]. The modeling system acts as a preprocessor. The user describes his problem in detail in a very verbal language, an opposite to a concise mathematical description of the problem. This p... |

51 |
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Citation Context ... a circle to points in the plane. The data points are artificially generated, adding random noise. The dashed circle is the theoretical circle. In NLPLIB a separable nonlinear least squares algorithm =-=[28]-=- is used to approximate positive sums of exponential functions to empirical data. To illustrate this facility we approximate two weighted exponential terms to the empirical data series by Steyn and Wy... |

49 |
ASCEND: An Object-Oriented Computer Environment for Modeling and Analysis: The Modeling Language
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Citation Context ...coded, computed by using numerical differences or nowadays using automatic differentiation techniques. In recent years several modeling languages has been developed, like AIMMS [6], AMPL [14], ASCEND =-=[27]-=-, GAMS [7, 9] and LINGO [1]. The modeling system acts as a preprocessor. The user describes his problem in detail in a very verbal language, an opposite to a concise mathematical description of the pr... |

36 |
Hybrid methods for nonlinear least squares
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(Show Context)
Citation Context ...orithm used is a modified version of the algorithm in Fletcher [12, chap. 2]. The prototype algorithms includes the following search step methods: ffl Gauss-Newton ffl Al-Baali-Fletcher hybrid method =-=[4]-=- ffl Fletcher-Xu hybrid method [13]. ffl Huschens method [23]. As shown in Holmstrom [22], the gn routine performs very well on ill conditioned non linear least squares problems compared to other rout... |

36 | Semidefinite programming - Todd |

32 | On the convergence of a sequential quadratic programming method with an augmented Lagrangian line search function
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(Show Context)
Citation Context ...re 1: Rosenbrocks banana with search steps and line search for Newtons method For general nonlinear problems with nonlinear constraints a sequential quadratic programming (SQP) method by Schittkowski =-=[30]-=- is implemented in routine consolve. Quadratic programming (QP) problems are solved with a standard active set method [25], routine qpi. In NLPLIB there are also two routines for solving QP with equal... |

28 | Hooking your solver to AMPL
- Gay
- 1997
(Show Context)
Citation Context ...and the standard set of test problems [8]. The CUTE distribution includes MATLAB interface routines. ffl TOMLAB interface to the AMPL model language[14]. The MATLAB Interface to AMPL was built by Gay =-=[15]-=-. ffl Integrated possibility to call to almost all routines in the MathWorks Optimization Toolbox. ffl You only need to define your problem once and use all available solvers! TOMLAB is described in m... |

20 |
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(Show Context)
Citation Context ...either been explicitly coded, computed by using numerical differences or nowadays using automatic differentiation techniques. In recent years several modeling languages has been developed, like AIMMS =-=[6]-=-, AMPL [14], ASCEND [27], GAMS [7, 9] and LINGO [1]. The modeling system acts as a preprocessor. The user describes his problem in detail in a very verbal language, an opposite to a concise mathematic... |

18 | Automatic determination of an initial trust region in nonlinear programming
- Sartenaer
- 1997
(Show Context)
Citation Context ... the Polak-Ribiere conjugate gradient method. Included is also a solver routine strustr that implements a structural trust region algorithm [10] combined with an initial trust region radius algorithm =-=[29]-=-. One of the menu options is to draw a contour plot of f(x) together with the search steps. On each search step there are marks for each trial value the line search algorithm has computed a function v... |

16 |
Convergence properties of minimization algorithms for convex constraints using a structured trust region
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(Show Context)
Citation Context ...erse BFGS, the Fletcher-Reeves conjugate gradient method and the Polak-Ribiere conjugate gradient method. Included is also a solver routine strustr that implements a structural trust region algorithm =-=[10]-=- combined with an initial trust region radius algorithm [29]. One of the menu options is to draw a contour plot of f(x) together with the search steps. On each search step there are marks for each tri... |

16 |
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(Show Context)
Citation Context ...er [12, chap. 2]. The prototype algorithms includes the following search step methods: ffl Gauss-Newton ffl Al-Baali-Fletcher hybrid method [4] ffl Fletcher-Xu hybrid method [13]. ffl Huschens method =-=[23]-=-. As shown in Holmstrom [22], the gn routine performs very well on ill conditioned non linear least squares problems compared to other routines, like leastsq in the Optimization Toolbox. In Figure 3 w... |

14 |
NLPLIB TB 1.0 - A MATLAB Toolbox for Nonlinear Optimization and Parameter Estimation
- Holmstrom
- 1997
(Show Context)
Citation Context ...he solution of optimization problems. TOMLAB features menu systems and driver routines for the most common optimization problems. TOMLAB has many internal algorithms implemented in the toolbox NLPLIB =-=[20]-=- and OPERA [21] and also calls routines from the MathWorks Optimization Toolbox [18]. It also provides interfaces to optimization software in FORTRAN and C/C++. This is possible using MEX-file interfa... |

14 | TOMLAB - A General Purpose, Open Matlab Environment for Research and Teaching in Optimization
- Holmström
- 1997
(Show Context)
Citation Context ...lity to call to almost all routines in the MathWorks Optimization Toolbox. ffl You only need to define your problem once and use all available solvers! TOMLAB is described in more detail in Holmstrom =-=[22]-=-. 3 The OPERA Toolbox The MATLAB toolbox OPERA is a collection of MATLAB m-files which solves many of the basic optimization problems in operations research and mathematical programming. Currently OPE... |

11 |
Algorithms for Nonlinear Least Squares - Particularly Problems with Constraints
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- 1983
(Show Context)
Citation Context ...also treat problems with bound constraints in a similar way as the routine ucsolve described in Section 4. If rank problems occur the prototype algorithm is using subspace minimization, see Lindstrom =-=[24]-=-. The line search algorithm used is a modified version of the algorithm in Fletcher [12, chap. 2]. The prototype algorithms includes the following search step methods: ffl Gauss-Newton ffl Al-Baali-Fl... |

9 |
TB 1.0 - A Matlab Toolbox for Optimization Algorithms in Operations Research
- OPERA
- 1997
(Show Context)
Citation Context ...optimization problems. TOMLAB features menu systems and driver routines for the most common optimization problems. TOMLAB has many internal algorithms implemented in the toolbox NLPLIB [20] and OPERA =-=[21]-=- and also calls routines from the MathWorks Optimization Toolbox [18]. It also provides interfaces to optimization software in FORTRAN and C/C++. This is possible using MEX-file interfaces. To solve o... |

6 |
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(Show Context)
Citation Context ...erical differences or nowadays using automatic differentiation techniques. In recent years several modeling languages has been developed, like AIMMS [6], AMPL [14], ASCEND [27], GAMS [7, 9] and LINGO =-=[1]-=-. The modeling system acts as a preprocessor. The user describes his problem in detail in a very verbal language, an opposite to a concise mathematical description of the problem. This problem descrip... |

4 |
Some methods for fitting compartment models to data. Technical report, Wetenskaplike bydraes van die pu vir cho, Potchefstroomse Universiteit vir CHO
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(Show Context)
Citation Context ...s used to approximate positive sums of exponential functions to empirical data. To illustrate this facility we approximate two weighted exponential terms to the empirical data series by Steyn and Wyk =-=[31]-=-. Figure 4 shows the first part of the series, the approximating 5 -5-4 -3-2 -1 0 1 2 3 4 5 -3 -2 -1 0 1 2 3 4 5 Approximating circle (100 points) and theoretical (red and dashed) x Figure 3: Using so... |

3 |
Optimization Toolbox User's Guide - For Use with MATLAB
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(Show Context)
Citation Context ...es for the most common optimization problems. TOMLAB has many internal algorithms implemented in the toolbox NLPLIB [20] and OPERA [21] and also calls routines from the MathWorks Optimization Toolbox =-=[18]-=-. It also provides interfaces to optimization software in FORTRAN and C/C++. This is possible using MEX-file interfaces. To solve optimization problems, traditionally the user has been forced to write... |

1 |
A Modeling Language for Mathematical Programming. The Scientific
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(Show Context)
Citation Context ...n explicitly coded, computed by using numerical differences or nowadays using automatic differentiation techniques. In recent years several modeling languages has been developed, like AIMMS [6], AMPL =-=[14]-=-, ASCEND [27], GAMS [7, 9] and LINGO [1]. The modeling system acts as a preprocessor. The user describes his problem in detail in a very verbal language, an opposite to a concise mathematical descript... |