Mathematical Programming

Course title

L0030000

Course description

Mathematical programming (MP) is a useful tool for optimization problems that appear everywhere in modern society. This course presents the theoretical framework and algorithms of mathematical programming for 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

To understand that programming problems in the real world can be formulated as mathematical programming problems, and to formulate simple problems by yourself. (Class schedule 1, 2, 3, 4, 5, 6)
To understand the simplex method and duality theorem, and to solve simple linear programming problems. (Class schedule 2,3)
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 the student can understand and explain the basic concepts explained in class (formulation of mathematical programming problems, the unit method and duality theorem, nonlinear programming problems) and solve problems at the same level as the examples covered in class, the student will receive 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 syllabus, and search applications of mathematical programming.	80minutes
1.		Review: Find an example yourself and formulate it into a linear programming problem.	80minutes
2.	Concepts, principle, and example of the simplex method	Preparation: Read Ref. (1) 2.2.	80minutes
2.	Concepts, principle, and example of the simplex method	Review: Explain “the simplex method” in your own words and try to find and apply examples.	80minutes
3.	Relaxation problem and duality theorem	Preparation: Read Ref. (1) 2.3	80minutes
3.	Relaxation problem and duality theorem	Review: Explain “the duality theorem” in your own words and try to find and apply examples.	80minutes
4.	Nonlinear programming problem	Preparation: Read Ref. (1) 3.1	80minutes
4.	Nonlinear programming problem	Review: Find an example yourself and formulate it into a nonlinear programming problem.	80minutes
5.	Optimization problem without constraints	Preparation: Read Ref. (1) 3.2	80minutes
5.	Optimization problem without constraints	Review: Explain “the optimization without constraints” in your own words and try to find and apply examples.	80minutes
6.	Optimization problem with constraints	Preparation: Read Ref. (1) 3.3	80minutes
6.	Optimization problem with constraints	Review: Explain “the optimization with constraints” in your own words and try to find and apply examples.	80minutes
7.	Final Exam and Comments	Review the contents of the 1th to the 6th lecture. You are expected to solve concrete problems if the general formula or algorithm is presented.	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

Lunch time between 2nd and 3rd periods on Monday. E-mail contact is also available to ask questions.

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 : Sat Mar 08 04:24:22 JST 2025