# Syllabus 2018

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Linear Programming

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Our syllabus can be seen at the website of KULASIS since 2019.

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## Course Title : Linear Programming

Code | 90690 |
---|---|

Course Year | 1st year |

Term | |

Class day & Period | |

Location | |

Credits | 2 |

Restriction | No Restriction |

Lecture Form(s) | Lecture |

Language | Japanese |

Instructor |

### Course Description

Lectures on modeling and algorithms of mathematical optimization, with main focus on linear programming, which is the most fundamental subject in system optimization.

### Grading

Based on the score of the term examination.

### Course Goals

To learn the basic ideas of formulating optimization models, and to understand theoretical properties and solution methods of linear programming.

### Course Topics

Theme | Class number of times | Description |
---|---|---|

Introduction to Mathematical Optimizaiton | 1 | Introduction to Mathematical Optimization. Reviews of some mathematics for linear programming, in particular, linear algebras. |

Mathematical Programming Models | 4 | Representative mathematical programming models such as linear programming models, network programming models, noninear programming models, and combinatorial programming models, with simple illustrative examples. |

Linear Programming and Basic Solutions | 2 | Formulation of linear programs in the standard form, and basic concepts of basic solutions, basic feasible solutions, and optimal basic solutions. |

Simplex Method | 3 | Basic ideas and concrete procedures of the simplex method that is a classical method for linear programming. Topics include two-stage linear programming, variables with upper bounds, and network simplex methods. |

Duality and Sensitivity Analysis | 3 | Duality as an important theory in linear programming, and sensitivity analysis as a useful technique in decision making. |

Interior Point Methods | 1 | Interior point methods as polynomial-time algorithms in linear programming. |

Review and Summary | 1 | Review and Summary. Confirmation of achievement level. |

### Textbook

Fukushima, M.: Introduction to Mathematical Programming: New Edition (in Japanese), Asakura Shoten .