Course title
L00300003
Mathematical Programming

 WATABE Shohei
Course description
Mathematical programming is an effective method for solving optimization problems that appear throughout modern society. Furthermore, the rapidly advancing field of artificial intelligence requires mathematical optimization techniques. This lecture will cover the theoretical framework and specific algorithms of mathematical programming, focusing on linear and nonlinear programming problems.
Purpose of class
To learn the basic solution methods of linear and nonlinear programming problems and to apply them to simple problems.
Goals and objectives
  1. To understand that real-world programming problems can be formulated as mathematical programming problems and to actually formulate these simple problems. (Class schedule 1, 2, 3, 4, 5, 6)
  2. To understand the simplex method and duality theorem, and to solve simple linear programming problems. (Class schedule 2,3)
  3. To understand optimization methods for nonlinear programming problems and to solve simple problems. (Class schedule 4,5,6)
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Check Tests Exam Total.
1. 10% 20% 30%
2. 10% 20% 30%
3. 20% 20% 40%
Total. 40% 60% -
Evaluation method and criteria
Grading: Check tests (40%) and final exam (60%). Over 60% in total is acceptable.
If you can understand and explain the basic concepts explained in class, such as formulation of mathematical programming problems, the simplex method and duality theorem, and nonlinear programming problems, and you solve problems whose levels are the same as examples treated in classes, you will be able to achieve a total score of 60% or higher.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Introduction of mathematical programing
Formulation of linear programming problem. 		Preparation: Read the relevant sections of the reference book and lecture materials in advance. 80minutes
Review: Go through the lecture content and complete the check test. 80minutes
2. Concepts, principle, and example of the simplex method Preparation: Read the relevant sections of the reference book and lecture materials in advance. 80minutes
Review: Go through the lecture content and complete the check test. 80minutes
3. Relaxation problem and duality theorem Preparation: Read the relevant sections of the reference book and lecture materials in advance. 80minutes
Review: Go through the lecture content and complete the check test. 80minutes
4. Nonlinear programming problem Preparation: Read the relevant sections of the reference book and lecture materials in advance. 80minutes
Review: Go through the lecture content and complete the check test. 80minutes
5. Optimization problem without constraints Preparation: Read the relevant sections of the reference book and lecture materials in advance. 80minutes
Review: Go through the lecture content and complete the check test. 80minutes
6. Optimization problem with constraints Preparation: Read the relevant sections of the reference book and lecture materials in advance. 80minutes
Review: Go through the lecture content and complete the check test. 80minutes
7. Final Exam and Comments Review the contents in Lectures from 1 to 6. 365minutes
Total. - - 1325minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
TEXTBOOK: S. Umetani, “Mathematical Optimization: From Models to Algorithms”, Kodan-sha (in Japanese)
REFERENCE BOOK: M. Kanatani, “Easy-to-understand mathematics of optimization” Kyoritsu Shuppan (in Japanese)
REFERENCE BOOK: T. Kuno, M. Shigeno, and J. Goto, “IT Text Mathematical Optimization” Ohm-sha (in Japanese)
Prerequisites
Understanding the contents of "Data Structure and Algorithms 2" and having a basic knowledge of calculus and linear algebras. Mathematical skills to deal with equations are also required.
Office hours and How to contact professors for questions
  • During the lunch break on lecture days, or via email.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
  • 12.RESPONSIBLE CONSUMPTION & PRODUCTION
Last modified : Thu Mar 06 10:05:27 JST 2025