# Models

## Contents

## The testprob collection[edit]

### Introduction[edit]

Each of the sections in this part will demonstrate a problem class. Most sections also have a small example in Matlab code with a formal mathematical problem description.

The functions `probInit` and `tomrun` respectively initializes and solves the problems in Matlab. For example:

Prob = probInit('gp_prob',1); tomRun('',Prob)

### Problems[edit]

- Linear Programming Problems: lp_prob
- Mixed-Integer Linear Programming Problems: mip_prob
- Quadratic Programming Problems: qp_prob
- Mixed-Integer Quadratic Programming Problems: mipq_prob
- Mixed-Integer Quadratic Programming Problems with Quadratic Constraints: miqq_prob
- Nonlinear Programming Problems: con_prob and chs_prob
- Mixed-Integer Nonlinear Programming Problems: minlp_prob
- Linear Least Squares Problems: lls_prob
- (Constrained) Nonlinear Least Squares Problems: cls prob, mgh_prob and ls_prob
- Global Optimization Problems: glb_prob, lgo1_prob, lgo2_prob and gkls_prob
- Constrained Global Optimization Problems: glc_prob
- Unconstrained Optimization: uc_prob and uhs_prob
- Linear Semi-Definite Programming Problem with Linear Matrix Inequalities: sdp_prob
- Linear Semi-Definite Programming Problem with Bilinear Matrix Inequalities: bmi_prob
- Constrained Goal Attainment Problems: goals_prob and mco_prob
- Geometric programming problems: gp_prob
- Fitting of positive sums of Exponentials: exp_prob

## The modellib collection[edit]

### Introduction[edit]

The bundle `modellib` is a collection of linear and mixed-integer programming problems. For each problem there are two m-files. One that formulate and define the problem with words and tables, and a second that interpret the tables into the standard `TOMLAB prob` format and solves it. In order to interpret the results a large amount of text is displayed explaining the x_k vector.

The problems in modellib are originally from a translation by Hickpe of the text "Programmation linare" by Gueret, Prins and Seveaux with the english title "Applications of optimization...".

### Problems[edit]

- Mining and Processing
- Scheduling
- Planning
- Loading and Cutting
- Ground transport
- Air transport
- Telecommunication
- Economics
- Timetabling
- Public Services

## Additional downloads: lp prob, milp prob and qp prob[edit]

At the TOMLAB downloads page three zip files with more problems can be found. Many of these are quite large and may be good as test cases for benchmarking. A package of about 250 MB with mixed LP/MILP are also available from your TOMLAB representative.