# Models

## Contents

## The testprob collection

### Introduction

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

- 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

### Introduction

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

- 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

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.