KA119001 System Optimization

Hiroshima University Syllabus

Japanese

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

Lecture Code KA119001 Subject Classification Specialized Education

Subject Name システム最適化

Subject Name
（Katakana）システムサイテキカ

Subject Name in
English System Optimization

Instructor MUKAIDANI HIROAKI

Instructor
(Katakana) ムカイダニ　ヒロアキ

Campus Higashi-Hiroshima Semester/Term 2nd-Year,  Second Semester,  3Term

Days, Periods, and Classrooms (3T) Mon9-10,Weds9-10：ENG 116

Lesson Style Lecture Lesson Style
(More Details) 　

Lecture

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 2 : Undergraduate Low-Intermediate

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords Optimization

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
（Abilities and Skills）
・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value.
・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis.

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 In this lecture, optimization is discussed to analyze mathematical sciences. By using these results, various operation which should be optimized is decided.

Class Schedule Lesson 1: What is an optimization problem?
Lesson 2: Unconstrained nonlinear optimization 1 (gradient vector and Hessian matrix)
Lesson 3: Unconstrained nonlinear optimization 2 (applied problems)
Lesson 4: Constrained nonlinear optimization (Lagrange multiplier method)
Lesson 5: Nonlinear optimization with inequality constraints (KKT conditions)
Lesson 6: Simultaneous Differential Equations
Lesson 7: Transition matrix
Lesson 8: Power series solutions
Lesson 9: Stability Theory
Lesson 10: Basics of stability
Lesson 11: Stability Theory of Physical Systems
Lesson 12: Discretization of differential equations
Lesson 13: Numerical solution of simultaneous differential equations
Lesson 14: Multidimensional Laplace Transform
Lesson 15: Partial Differential Equations Theory

Text/Reference
Books,etc. 新刊「基礎履修  応用数学」向谷・下村・相澤
ISBN９７８−４−５６３−０１１７２−７

PC or AV used in
Class,etc. 　

(More Details) blackboard

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review For each lecture, the review should be needed by reading the text book. Furthermore, the practical calculation and simulation would be helpful.

Lesson 1: Understand the meaning and purpose of optimization through specific examples of various optimization problems.
Lesson 2: Be able to calculate gradient vectors, Hessian matrices, etc., and derive optimization conditions.
Lesson 3: Recognize the importance of optimization by solving applied problems (least squares method and principal analysis).
Lesson 4: Understand the Lagrangian multiplier method and be able to derive optimization conditions.
Lesson 5: Inequality constraints can be processed using KKT.
Lesson 6: Being able to describe and solve higher-order differential equations using simultaneous differential equations.
Lesson 7: Using a transition matrix, you can display an exponential matrix.
Lesson 8: Using power series solutions, you will be able to analyze differential equations that cannot be expressed using analytical solutions.
Lesson 9: Start with the definition of stability theory and be aware of its application in the real world.
Lesson 10: Understand the importance of stability by cultivating the basics of stability in actual dynamic systems.
Lesson 11: Through practice problems, students should be able to understand various physical phenomena and discuss the theory of stability of physical systems.
Lesson 12: Confirm that differential equations can be solved numerically by discretizing them.
Lesson 13: Understand that higher-order differential equations can be found by numerically solving simultaneous differential equations using Euler's method and Runge-Kutta method.
Lesson 14: Solving simultaneous differential equations using multidimensional Laplace transform.
Lesson 15: Be able to solve simple partial differential equations using the basics of differential equations.

Requirements Calculus and Linear Algebra are mandatory.

Grading Method Mini-tests (10%) and Final exam (90%)

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	2024Year	School/Graduate School	School of Informatics and Data Science
Lecture Code	KA119001	Subject Classification	Specialized Education
Subject Name	システム最適化
Subject Name （Katakana）	システムサイテキカ
Subject Name in English	System Optimization
Instructor	MUKAIDANI HIROAKI
Instructor (Katakana)	ムカイダニ　ヒロアキ
Campus	Higashi-Hiroshima	Semester/Term	2nd-Year, Second Semester, 3Term
Days, Periods, and Classrooms	(3T) Mon9-10,Weds9-10：ENG 116
Lesson Style	Lecture	Lesson Style (More Details)
Lecture
Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	2 : Undergraduate Low-Intermediate
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords	Optimization
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 （Abilities and Skills）・A. Information infrastructure development technology, information processing technology, technology that analyzes data and creates new added value. ・B. Ability to identify new problems independently and solve them through quantitative and logical thinking based on data, multifaceted perspectives, and advanced information processing and analysis. 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	In this lecture, optimization is discussed to analyze mathematical sciences. By using these results, various operation which should be optimized is decided.
Class Schedule	Lesson 1: What is an optimization problem? Lesson 2: Unconstrained nonlinear optimization 1 (gradient vector and Hessian matrix) Lesson 3: Unconstrained nonlinear optimization 2 (applied problems) Lesson 4: Constrained nonlinear optimization (Lagrange multiplier method) Lesson 5: Nonlinear optimization with inequality constraints (KKT conditions) Lesson 6: Simultaneous Differential Equations Lesson 7: Transition matrix Lesson 8: Power series solutions Lesson 9: Stability Theory Lesson 10: Basics of stability Lesson 11: Stability Theory of Physical Systems Lesson 12: Discretization of differential equations Lesson 13: Numerical solution of simultaneous differential equations Lesson 14: Multidimensional Laplace Transform Lesson 15: Partial Differential Equations Theory
Text/Reference Books,etc.	新刊「基礎履修応用数学」向谷・下村・相澤 ISBN９７８−４−５６３−０１１７２−７
PC or AV used in Class,etc.
(More Details)	blackboard
Learning techniques to be incorporated
Suggestions on Preparation and Review	For each lecture, the review should be needed by reading the text book. Furthermore, the practical calculation and simulation would be helpful. Lesson 1: Understand the meaning and purpose of optimization through specific examples of various optimization problems. Lesson 2: Be able to calculate gradient vectors, Hessian matrices, etc., and derive optimization conditions. Lesson 3: Recognize the importance of optimization by solving applied problems (least squares method and principal analysis). Lesson 4: Understand the Lagrangian multiplier method and be able to derive optimization conditions. Lesson 5: Inequality constraints can be processed using KKT. Lesson 6: Being able to describe and solve higher-order differential equations using simultaneous differential equations. Lesson 7: Using a transition matrix, you can display an exponential matrix. Lesson 8: Using power series solutions, you will be able to analyze differential equations that cannot be expressed using analytical solutions. Lesson 9: Start with the definition of stability theory and be aware of its application in the real world. Lesson 10: Understand the importance of stability by cultivating the basics of stability in actual dynamic systems. Lesson 11: Through practice problems, students should be able to understand various physical phenomena and discuss the theory of stability of physical systems. Lesson 12: Confirm that differential equations can be solved numerically by discretizing them. Lesson 13: Understand that higher-order differential equations can be found by numerically solving simultaneous differential equations using Euler's method and Runge-Kutta method. Lesson 14: Solving simultaneous differential equations using multidimensional Laplace transform. Lesson 15: Be able to solve simple partial differential equations using the basics of differential equations.
Requirements	Calculus and Linear Algebra are mandatory.
Grading Method	Mini-tests (10%) and Final exam (90%)
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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