Numbering Code	G-INF04 53424 LJ54 G-INF04 53424 LJ10	Year/Term	2022 ・ Second semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Thu.2
Instructor name	FUKUDA HIDEMI (Graduate School of Informatics Associate Professor) HARAGUCHI KAZUYA (Graduate School of Informatics Associate Professor)
Outline and Purpose of the Course	This course will be an introduction to mathematical programming with an emphasis on basic theories for nonlinear programming and efficient techniques for the solution of combinatorial optimization. The first half of the course will consist in optimality conditions, and concrete proof for the Karush-Kuhn-Tucker conditions. We will also discuss methods that use these conditions, as well as duality theory, and applications of duality. The second half illustrates representative methods for the integer optimization problem and their mathematical background. The contents include branch-and-bound, cutting plane, Lagrangian dual based method, and column generation.
Course Goals	In the first part of this class, we will learn optimality conditions, some methods and duality theory for nonlinear optimization problems. In the second part of this class, we will learn representative methods for the integer optimization problem and their mathematical background.
Schedule and Contents	1. Convex analysis, first-order optimality conditions 2. Proof of the Karush-Kuhn-Tucker conditions 3. Optimality conditions and constraint qualifications 4. Basics in nonlinear programming methods 5. Some methods for nonlinear programming (1) 6. Some methods for nonlinear programming (2) 7. Duality theory 8. Applications of duality theory 9. Branch-and-bound 10. Cutting-plane method (1) 11. Cutting-plane method (2) 12. Branch-and-cut 13. Lagrangian dual based method 14. Column generation (1) 15. Column generation (2) Instructor for class 1 to 8: Fukuda Instructor for class 9 to 15: Haraguchi
Evaluation Methods and Policy	Two reports, one for the nonlinear programming, and one for the discrete optimization part. It may include additional short reports too.
Course Requirements	None
Study outside of Class (preparation and review)	Not applicable
References, etc.	非線形最適化の基礎, 福島雅夫, (朝倉書店, 2001), ISBN:978-4254280012 非線形計画法, 山下信雄, (朝倉書店, 2015), ISBN:978-4254117912 Integer Programming, L. A. Wolsey, (Wiley Inter Science，1998), ISBN:978-0471283669