Mathematical Programming

Course title

33014300

Middle-level Diploma Policy (mDP)

Program / Major	mDP	Goals
IoT Course	DP-4a・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Software Course	DP-4b・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Media Course	DP-4c・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Data Science Course	DP-4d・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Mechatronics Course	DP-4・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Architecture and Architectural Engineering Course	DP-4a・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Environmental Systems and Urban Planning Course	DP-4b・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Bioscience Course	DP-4a・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Biomedical Engineering Course	DP-4b・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Sports Engineering Course	DP-4c・3	専門分野と他分野を関連付ける素養主軸となる分野の専門知識を他分野と関連付ける分野横断型の知識と行動力を修得し、社会で活用できる。
Mathematical Sciences Course	DP-4・2	キャリアを見据えた高度な専門知識現象の背後にある数理構造やデータのパターンを理論的に解析し、社会や自然科学、工学における複雑な課題に対して数理的視点から解決戦略を提案できる。

Purpose of class

Deliver lectures about problem formulation of mathematical programming, fundamental idea and approach to linear and nonlinear mathematical programming problems.

Introduce numerical solutions by using MATLAB, and by the descent method.

Aim to provide practical formulations and solutions for students.

Course description

Mathematical programming is used to maximize or minimize a function under given conditions (constraints). In this course, we explain the problem formulation of mathematical programming, and then talk about some basic approach to solving both linear and nonlinear mathematical programming problems. Numerical methods by using MATLAB solvers and the descent method are also introduced.

Goals and objectives

Students can understand the problem formulation and describe the representation of mathematical programming.
Students can understand the basic idea of linear mathematical programming and can solve the problems by using graphical approach and the simplex method.
Students can understand the basic idea of nonlinear mathematical programming and can manage to obtain the analytic solutions and the numerical solutions.

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Mid-term exam	Final exam	Quizzes in class	Total.
1.	15%	10%	5%	30%
2.	15%	15%	10%	40%
3.		25%	5%	30%
Total.	30%	50%	20%	-

Evaluation method and criteria

Mid-term exam: 30%, Final exam: 50% Quizzes in class: 20%

Pass when reaching 60% of the whole evaluation, or in other words, reaching the level of describing problem formulation of mathematical programming, solving simple mathematical programming problems in both linear and nonlinear cases.

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Guidance, mathematical programming models	Prepare mathematical programming models	190minutes
2.	Minimize functions with one or two variables	Review of basic calculus, functions and their extreme value points	190minutes
3.	Mathematical Linear Programming (MLP) 1: various MLP models	Prepare various MLP models and the problems	190minutes
4.	Mathematical Linear Programming (MLP) 2: general problem formulation and graphical solution	Prepare general problem formulation and graphical solution	190minutes
5.	Mathematical Linear Programming (MLP) 3: simplex method	Review linear equations, prepare the simplex method	190minutes
6.	Mathematical Linear Programming (MLP) 4: solution by MATLAB solvers; Mid-term exam	Prepare the problem formulation and solution by Excel solvers	190minutes
7.	Duality and sensitivity analysis 1: duality and its economic interpretation	Prepare the definition of duality and its economic interpretation	190minutes
8.	Duality and sensitivity analysis 2: sensitivity analysis	Prepare sensitivity analysis	190minutes
9.	Application of Mathematical Linear Programming (MLP) 1: two-stage simplex method	Prepare two-stage simplex method	190minutes
10.	Application of Mathematical Linear Programming (MLP) 2: game theory	Review basic optimization problem, and prepare game theory	190minutes
11.	Mathematical Nonlinear Programming (MNP) 1: optimal condition of functions with one variable	Review and prepare the optimal condition of functions with one variable	190minutes
12.	Mathematical Nonlinear Programming (MNP) 2: optimal condition of functions with two variables	Review and prepare the optimal condition of functions with two variables	190minutes
13.	Mathematical Nonlinear Programming (MNP) 3: steepest descent method	Prepare the steepest descent method	190minutes
14.	Review and exercise of the whole course, final exam	Review of the whole course	190minutes
Total.	-	-	2660minutes

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
Feedback in/outside the class.

Textbooks and reference materials

Textbook:
Sakawa, Yano, Nishizaki: Easy-To-Understood Mathematical Programming, Morikita Publishing (ISBN 978-4-627-91771-2)

Reference Book:
Fukushima: Introduction to Mathematical Programming (New Version), Asakura Publishing (ISBN 978-4-254-28004-3)

Prerequisites

Office hours and How to contact professors for questions