授業の目的 【日本語】
Goals of the Course(JPN) | | |
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授業の目的 【英語】
Goals of the Course | | | This course offers a practical introduction to linear optimization. On the basis of several real-world applications, it is shown how linear programs are formulated, and how these can be solved by means of computer algorithms. The classical simplex algorithm is the method of choice for cardinal welfare maximization problems. Its multiobjective generalizations are used for ordinal Pareto optimization. Students will train their practical problem solving skills in an optimization project that spans over the course of the semester. |
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到達目標 【日本語】
Objectives of the Course(JPN) | | | Students will acquire the skills necessary to solve linear programs numerically. After successful completion of this course, students will be able to solve several well-known problems in economics and operations research, including but not limited to assignment problems, reallocation problems, transportation problems, and network flow problems. |
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授業の内容や構成
Course Content / Plan | | Week 1: Introduction
Week 2: Vector Spaces
Week 3: Systems of Linear Inequalities
Week 4: Linear Programming
Week 5: Simplex Algorithm
Week 6: Duality
Week 7: Assignment Problem
Week 8: House Market
Week 9: Pareto Efficiency
Week 10: Multiobjective Linear Programming
Week 11: Cardinal Welfare Maximization
Week 12: Cooperative Games
Week 13: Multiobjective Simplex Algorithm
Week 14: Normal Cone Algorithm
Week 15: |
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履修条件・関連する科目
Course Prerequisites and Related Courses | | | This seminar is open only to G30 undergraduate students. |
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成績評価の方法と基準
Course Evaluation Method and Criteria | | Each student has to report the progress on their optimization project during the weekly seminars. In addition, a graded presentation of their project results must be given at the end of the semester. Students must be able to demonstrate their understanding of the chosen method, and to explain their own program code, in order to pass this course.
Student Presentations: 100% |
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教科書・参考書
Textbook/Reference Book | | There is no designated textbook for this course. The following two books are a useful reference for students who want to deepen their understanding of the course topics.
The Theory of Linear Economic Models / David Gale : University of Chicago Press, 1960,
ISBN: 9780070227286
Multiobjective Linear Programming / Dinh The Luc : Springer, 2016,
ISBN: 9783319210902 |
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課外学習等（授業時間外学習の指示）
Study Load(Self-directed Learning Outside Course Hours) | | | Two hours of out-of-class work on the assigned optimization problem are required per week. |
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注意事項
Notice for Students | | | Supplementary course material will be provided online. |
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授業開講形態等
Lecture format, etc. | | |
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遠隔授業（オンデマンド型）で行う場合の追加措置
Additional measures for remote class (on-demand class) | | | Will be announced if necessary. |
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質問への対応方法
Office hour | | | Office hours by appointment via email. |
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