K5130010 Mathematical Optimization

Hiroshima University Syllabus

Japanese

Academic Year 2025Year School/Graduate School School of Engineering

Lecture Code K5130010 Subject Classification Specialized Education

Subject Name 数理最適化

Subject Name
（Katakana）スウリサイテキカ

Subject Name in
English Mathematical Optimization

Instructor KITAMURA MITSURU,KATAGIRI KAZUAKI

Instructor
(Katakana) キタムラ　ミツル,カタギリ　カズアキ

Campus Higashi-Hiroshima Semester/Term 2nd-Year, Second Semester, 4Term

Days, Periods, and Classrooms (4T) Thur5-8：ENG 116

Lesson Style Lecture Lesson Style
(More Details) Face-to-face

Credits 2.0 Class Hours/Week 4 Language of Instruction J : Japanese

Course Level 3 : Undergraduate High-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 10 : Integrated Engineering

Eligible Students 2nd year students

Keywords SDG_09, Optimization

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students) This is an elective required course in the Transportation Systems Program.
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Program of Transportation Systems
（Knowledge and Understanding）
・The area of systems: Technical knowledge on systems, information and transportation systems relating to transportation equipment and coexistence with the environment
（Abilities and Skills）
・The area of systems: The ability to apply technical knowledge of systems, information and transportation systems to solve issues relating to the areas of transportation equipment and coexistence with the environment

Class Objectives
/Class Outline 1. You will be able to understand objective functions, design variables, and constraints for optimization, and to logically organize and analyze planning problems.
2. You will be able to solve linear programming problems using the simplex method.
3. You will be able to solve unconstrained nonlinear programming problems using function gradients, Taylor series expansions, conjugate direction methods, and Newton's method.
4. You will be able to solve nonlinear programming problems with constraints using the SUMT method, Lagrange's undetermined multiplier method, and sequential quadratic programming.
5. You will be able to solve nonlinear programming problems with inequality conditions using a genetic algorithm.
6. You will be able to evaluate the suitability of design proposals using the various analysis methods listed above.

Class Schedule 1. Objectives and goals of this lecture: Calculations and graph creation using Excel
2. Objective functions, design variables, constraints, graphical solutions to linear programming problems
3. Slack variables, simplex method
4. Taylor series expansion, numerical differentiation
5. Linear line search, golden section method, quadratic interpolation method
6. Steepest descent method, Newton method
7. Midterm exam
8. Quasi-Newton method
9. Conjugate gradient method
10. Penalty function method, SUMT method
11. Lagrange's undetermined multiplier method
12. Problems with inequality constraints
13. Sequential quadratic programming
14. Genetic algorithms
15. Genetic algorithms (group work)

Midterm exam (30%), final exam (50%), and homework (20%).

Text/Reference
Books,etc. A must-have textbook: "Optimization by Mathematical Programming, Morikita Publishing, by Mitsuru Kitamura".

PC or AV used in
Class,etc. Text, Handouts

(More Details) A must-have textbook, handouts, PC(Excel)

Learning techniques to be incorporated

Suggestions on
Preparation and
Review Students will deepen their understanding through exercises using Excel during the lectures.
Homework assigned each time will serve as a review of the lesson.

Requirements

Grading Method Your grade is evaluated based on midterm exam (30%), final exam (50%), and homework (20%). Credits will be awarded for scores above 60%.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2025Year	School/Graduate School	School of Engineering
Lecture Code	K5130010	Subject Classification	Specialized Education
Subject Name	数理最適化
Subject Name （Katakana）	スウリサイテキカ
Subject Name in English	Mathematical Optimization
Instructor	KITAMURA MITSURU,KATAGIRI KAZUAKI
Instructor (Katakana)	キタムラ　ミツル,カタギリ　カズアキ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 4Term
Days, Periods, and Classrooms	(4T) Thur5-8：ENG 116
Lesson Style	Lecture	Lesson Style (More Details)	Face-to-face

Credits	2.0	Class Hours/Week	4	Language of Instruction	J : Japanese
Course Level	3 : Undergraduate High-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	10 : Integrated Engineering
Eligible Students	2nd year students
Keywords	SDG_09, Optimization
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)	This is an elective required course in the Transportation Systems Program.
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Program of Transportation Systems （Knowledge and Understanding）・The area of systems: Technical knowledge on systems, information and transportation systems relating to transportation equipment and coexistence with the environment （Abilities and Skills）・The area of systems: The ability to apply technical knowledge of systems, information and transportation systems to solve issues relating to the areas of transportation equipment and coexistence with the environment
Class Objectives /Class Outline	1. You will be able to understand objective functions, design variables, and constraints for optimization, and to logically organize and analyze planning problems. 2. You will be able to solve linear programming problems using the simplex method. 3. You will be able to solve unconstrained nonlinear programming problems using function gradients, Taylor series expansions, conjugate direction methods, and Newton's method. 4. You will be able to solve nonlinear programming problems with constraints using the SUMT method, Lagrange's undetermined multiplier method, and sequential quadratic programming. 5. You will be able to solve nonlinear programming problems with inequality conditions using a genetic algorithm. 6. You will be able to evaluate the suitability of design proposals using the various analysis methods listed above.
Class Schedule	1. Objectives and goals of this lecture: Calculations and graph creation using Excel 2. Objective functions, design variables, constraints, graphical solutions to linear programming problems 3. Slack variables, simplex method 4. Taylor series expansion, numerical differentiation 5. Linear line search, golden section method, quadratic interpolation method 6. Steepest descent method, Newton method 7. Midterm exam 8. Quasi-Newton method 9. Conjugate gradient method 10. Penalty function method, SUMT method 11. Lagrange's undetermined multiplier method 12. Problems with inequality constraints 13. Sequential quadratic programming 14. Genetic algorithms 15. Genetic algorithms (group work) Midterm exam (30%), final exam (50%), and homework (20%).
Text/Reference Books,etc.	A must-have textbook: "Optimization by Mathematical Programming, Morikita Publishing, by Mitsuru Kitamura".
PC or AV used in Class,etc.	Text, Handouts
(More Details)	A must-have textbook, handouts, PC(Excel)
Learning techniques to be incorporated
Suggestions on Preparation and Review	Students will deepen their understanding through exercises using Excel during the lectures. Homework assigned each time will serve as a review of the lesson.
Requirements
Grading Method	Your grade is evaluated based on midterm exam (30%), final exam (50%), and homework (20%). Credits will be awarded for scores above 60%.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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