KA118001 Mathematical Programming

Hiroshima University Syllabus

Japanese

Academic Year 2024Year School/Graduate School School of Informatics and Data Science

Lecture Code KA118001 Subject Classification Specialized Education

Subject Name 数理計画法

Subject Name
（Katakana）スウリケイカクホウ

Subject Name in
English Mathematical Programming

Instructor NISHIZAKI ICHIRO

Instructor
(Katakana) ニシザキ　イチロウ

Campus Higashi-Hiroshima Semester/Term 2nd-Year, First Semester, 1Term

Days, Periods, and Classrooms (1T) Weds3-4,Fri1-2：ECON B255

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture
Lectures are conducted face-to-face or on-demand.

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

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 11 : Electrical, Systems, and Control Engineering

Eligible Students Students enrolled in and before 2023

Keywords Linear programming, simplex method, two-phase simplex method, dual simplex method, integer programming, branch and bound method, nonlinear programming, Kuhn-Tucker conditions, Lagrangian function, descent method

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
(Applicable only to targeted subjects for undergraduate students)
Criterion referenced
Evaluation
(Applicable only to targeted subjects for undergraduate students) Computer Science Program
（Comprehensive Abilities）
・D2. Ability to derive optimal system solutions based on abundant cutting-edge information technologies for cross-sectoral issues in a diversified and complicated information society.

Data Science Program
（Comprehensive Abilities）
・D3. Ability to overlook social needs and issues that are intertwined in a complex manner and to solve issues with quantitative and logical thinking based on data, a multifaceted perspective, and advanced information analysis ability.

Intelligence Science Program
（Comprehensive Abilities）
・D3. Ability to grasp complexly intertwined social needs and issues from a bird's-eye view and solve issues with a multifaceted perspective and analytical ability based on a wide range of knowledge in intelligent science.

Class Objectives
/Class Outline Explanation and practice of mathematical programming theory which is one of most basic systems optimization methods

Class Schedule lesson1 Linear programming: Summary of mathematical programming
lesson2 Linear programming: Algebraic computations and definitions of linear programming problems
lesson3 Linear programming: Theory and algorithm of simplex method
lesson4 Linear programming: Theory and algorithm of two-phase method
lesson5 Linear programming: Theory and algorithm of dual simplex method
lesson6 Integer programming: Modelling based on integer programming probmes
lesson7 Integer programming: Basic framework of integer programming
lesson8 Integer programming: Theory and algorithm of branch and bound method
lesson9 Practices of linear and integer programming
lesson10 Intermediate exam (linear and integer programming)
lesson11 Nonlinear programming: Nonlinear programming problems and their conceptual foundations
lesson12 Nonlinear programming: Optimality condition for constrained and non-constrained optimization problems
lesson13 Nonlinear programming: Algorithm for solving non-constrained optimization problems
lesson14 Nonlinear programming: Algorithm for solving nonlinear programming problems
lesson15 Practices of nonlinear programming

Intermediate and final examinations, assignments

Text/Reference
Books,etc. Textbook: Masatoshi Sakawa and Ichiro Nishizaki, ``Introduction to Mathematical Programming'', Morikita Publishing Co., Ltd. (in Japanese)

PC or AV used in
Class,etc. 　

(More Details) Textbook, PC, projector

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review 1. Understand examples of mathematical programming problems in the real world
2. Learn basic concepts and terms about linear programming problems
3. Understand assumptions, the principle and the algorithm of simplex method by applying it to examples
4. Understand the principle and the algorithm of two-phase simplex method by applying it to examples
5. Understand the principle and the algorithm of dual simplex method by applying it to examples
6. Understand the formulation process of actual optimization problems as integer programming problems
7. Learn basic concepts and terms about integer programming problems
8. Understand the principle and the algorithm of branch and bound method by applying it to examples
9. Master the optimization methods for linear and integer programming problems by exercises
10. Understand the optimization methods for linear and integer programming problems
11. Understand the formulation process of actual optimization problems as nonlinear programming problems
12. Understand Kuhn-Tucker conditions and Lagrangian function
13. Understand the principle and the algorithm of descent method and Newton method by applying them to examples
14. Understand the principle and the algorithm of penalty method and generalized reduced gradient method by applying them to examples
15. Master the optimization methods for nonlinear programming problems by exercises

Requirements 1. Attendance at all classes is necessary or watch all videos.
2. Submit assignments.
2. An elementary knowledge of mathematics is necessary.

Grading Method Intermediate and final examinations, and assignments, the passing mark is 60.

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other Support: Tomohiro Hayashida (Office: A1-243，Extension Number: 5267，Email: hayashida@hiroshima-u.ac.jp)

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	2024Year	School/Graduate School	School of Informatics and Data Science
Lecture Code	KA118001	Subject Classification	Specialized Education
Subject Name	数理計画法
Subject Name （Katakana）	スウリケイカクホウ
Subject Name in English	Mathematical Programming
Instructor	NISHIZAKI ICHIRO
Instructor (Katakana)	ニシザキ　イチロウ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, First Semester, 1Term
Days, Periods, and Classrooms	(1T) Weds3-4,Fri1-2：ECON B255
Lesson Style	Lecture	Lesson Style (More Details)
Lecture Lectures are conducted face-to-face or on-demand.
Credits	2.0	Class Hours/Week		Language of Instruction	J : Japanese
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	11 : Electrical, Systems, and Control Engineering
Eligible Students	Students enrolled in and before 2023
Keywords	Linear programming, simplex method, two-phase simplex method, dual simplex method, integer programming, branch and bound method, nonlinear programming, Kuhn-Tucker conditions, Lagrangian function, descent method
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program (Applicable only to targeted subjects for undergraduate students)
Criterion referenced Evaluation (Applicable only to targeted subjects for undergraduate students)	Computer Science Program （Comprehensive Abilities）・D2. Ability to derive optimal system solutions based on abundant cutting-edge information technologies for cross-sectoral issues in a diversified and complicated information society. Data Science Program （Comprehensive Abilities）・D3. Ability to overlook social needs and issues that are intertwined in a complex manner and to solve issues with quantitative and logical thinking based on data, a multifaceted perspective, and advanced information analysis ability. Intelligence Science Program （Comprehensive Abilities）・D3. Ability to grasp complexly intertwined social needs and issues from a bird's-eye view and solve issues with a multifaceted perspective and analytical ability based on a wide range of knowledge in intelligent science.
Class Objectives /Class Outline	Explanation and practice of mathematical programming theory which is one of most basic systems optimization methods
Class Schedule	lesson1 Linear programming: Summary of mathematical programming lesson2 Linear programming: Algebraic computations and definitions of linear programming problems lesson3 Linear programming: Theory and algorithm of simplex method lesson4 Linear programming: Theory and algorithm of two-phase method lesson5 Linear programming: Theory and algorithm of dual simplex method lesson6 Integer programming: Modelling based on integer programming probmes lesson7 Integer programming: Basic framework of integer programming lesson8 Integer programming: Theory and algorithm of branch and bound method lesson9 Practices of linear and integer programming lesson10 Intermediate exam (linear and integer programming) lesson11 Nonlinear programming: Nonlinear programming problems and their conceptual foundations lesson12 Nonlinear programming: Optimality condition for constrained and non-constrained optimization problems lesson13 Nonlinear programming: Algorithm for solving non-constrained optimization problems lesson14 Nonlinear programming: Algorithm for solving nonlinear programming problems lesson15 Practices of nonlinear programming Intermediate and final examinations, assignments
Text/Reference Books,etc.	Textbook: Masatoshi Sakawa and Ichiro Nishizaki, ``Introduction to Mathematical Programming'', Morikita Publishing Co., Ltd. (in Japanese)
PC or AV used in Class,etc.
(More Details)	Textbook, PC, projector
Learning techniques to be incorporated
Suggestions on Preparation and Review	1. Understand examples of mathematical programming problems in the real world 2. Learn basic concepts and terms about linear programming problems 3. Understand assumptions, the principle and the algorithm of simplex method by applying it to examples 4. Understand the principle and the algorithm of two-phase simplex method by applying it to examples 5. Understand the principle and the algorithm of dual simplex method by applying it to examples 6. Understand the formulation process of actual optimization problems as integer programming problems 7. Learn basic concepts and terms about integer programming problems 8. Understand the principle and the algorithm of branch and bound method by applying it to examples 9. Master the optimization methods for linear and integer programming problems by exercises 10. Understand the optimization methods for linear and integer programming problems 11. Understand the formulation process of actual optimization problems as nonlinear programming problems 12. Understand Kuhn-Tucker conditions and Lagrangian function 13. Understand the principle and the algorithm of descent method and Newton method by applying them to examples 14. Understand the principle and the algorithm of penalty method and generalized reduced gradient method by applying them to examples 15. Master the optimization methods for nonlinear programming problems by exercises
Requirements	1. Attendance at all classes is necessary or watch all videos. 2. Submit assignments. 2. An elementary knowledge of mathematics is necessary.
Grading Method	Intermediate and final examinations, and assignments, the passing mark is 60.
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other	Support: Tomohiro Hayashida (Office: A1-243，Extension Number: 5267，Email: hayashida@hiroshima-u.ac.jp)
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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