Numbering Code	P-MGT75 60045 LJ55	Year/Term	2022 ・ Second semester
Number of Credits	2	Course Type	Lecture
Target Year		Target Student
Language	Japanese	Day/Period	Wed.2
Instructor name	NAGAMOCHI HIROSHI (Graduate School of Informatics Professor) YAMASHITA NOBUO (Graduate School of Informatics Professor) HARAGUCHI KAZUYA (Graduate School of Informatics Associate Professor)
Outline and Purpose of the Course	Mathematical programming or optimization is a methodology for modeling a real-world problem as a mathematical problem with an objective function and constraints, and solving it by some suitable procedure (algorithm). This course consists of lectures on basic theory and methods in nonlinear optimization and combinatorial optimization.
Course Goals	To understand basic theory and algorithms in continuous optimization and combinatorial optimization.
Schedule and Contents	- Fundamentals of nonlinear optimization (2 times) Basic notions in continuous optimization such as global and local minima, convex sets and functions, gradients and Hessian matrices of multivariate functions. - Method of unconstrained optimization (2) Basic unconstrained optimization methods such as steepest descent method, Newton's method, quasi-Newton methods, conjugate gradient method. - Optimality conditions and duality (2) Optimality conditions for constrained optimization problems, called Karush-Kuhn-Tucker conditions, as well as the second-order optimality conditions and Lagrangian duality theory. - Methods of constrained optimization (1) Basic methods of constrained optimization such as penalty methods and sequential quadratic programing methods. - Combinatorial optimization (1) Typical combinatorial optimization problems such as traveling salesman problem and knapsack problem, and their computational complexity. - Branch-and-bound method and dynamic programming 2 Basic exact solution strategies for combinatorial optimization such as branch-and-bound method and dynamic programming. - Approximation algorithms (3) Approximation algorithms for hard combinatorial optimization problems, and their theoretical performance guarantees. - Summary and review (1) Summary and review. Confirmation of achievement level.
Evaluation Methods and Policy	Report score and end-term examination
Course Requirements	Linear Programming recommended.
Study outside of Class (preparation and review)	No particular preparation or review is required. But ask your question while or after lecture whenever you get some question.
References, etc.	Introduction to Mathematical Programming: New Edition (in Japanese), M. Fukushima, (Asakura Shoten) Combinatorial Optimization - Metaheuristic Algorithms (in Japanese), M. Yagiura and T. Ibaraki, (Asakura Shoten)