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最適化・意思決定論

Mathematical optimization in Operations Research
Operations Research (O.R.) is the application of scientific and mathematical methods to the study and analysis of problems involving complex systems (according to The Institute for Operations Research and the Management Sciences). Among many mathematical methods and tools in O.R., the most fundamental is the concept of optimization. It is to search for the best choice among possible alternatives under certain conditions and constraints. In the mathematical language, it is to maximize or minimize a given objective function by controlling decision variables under the set of constraints. Optimization theory is also a part of applied mathematics, and is widely employed in academic disciplines that deal with mathematical modeling of human decision making. In particular, it plays an essential role in economics for its descriptions of economic decision making and valuation.
In this lecture, students will learn the theories of mathematical optimization as methods in O.R. The lecture starts with providing an overview of O.R. with an emphasis on optimization methods. It moves on to the theory of static optimization. The third part of the lecture discusses the theory of dynamic optimization.
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時間割/共通科目コード
コース名
教員
学期
時限
08D1426
FAS-DA4F26L3
最適化・意思決定論
前田 章
A1 A2
水曜2限
マイリストに追加
マイリストから削除
教室
講義使用言語
英語
単位
2
実務経験のある教員による授業科目
NO
他学部履修
開講所属
教養学部
授業計画
1. Introduction to O.R. and optimization Part I: Linear programing 2. The simplex method 3. Sensitivity analysis Part II: Nonlinear optimization theory 4. The Lagrange method 5. The Karush-Kuhn-Tucker (KKT) conditions 6. Duality 7. The envelope theorem 8. Multi-objective optimization Part III: Dynamic optimization 9. Calculus of variations 10. The maximum principle 11. Dynamic programming 12. Dynamical systems 13. Stochastic dynamic optimization
授業の方法
Lectures
成績評価方法
Evaluation is based on take-home final exam (assignment). There will be no online exam. The details will be announced in due course.
教科書
No textbook. Handouts are available on ITC-LMS.
参考書
Recommended readings: Hillier, F. S. and G. J. Lieberman. Introduction to Operations Research, 10th Edition. McGraw Hill Higher Education, 2014. Intriligator, M.D. Mathematical Optimization and Economic Theory. Society for Industrial and Applied Mathematics, 2002. Sundaram, R.K. A First Course in Optimization Theory. Cambridge University Press, 1996.
履修上の注意
Junior-Division math courses or similar level of calculus and linear algebra are prerequisite.