Course title
V04605002
Mathematical Programming

 ZHAI GUISHENG Click to show questionnaire result at 2019
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 Excel solvers are also introduced.
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 Excel solvers, and by the descent method.

Aim to provide practical formulations and solutions for students.
Goals and objectives
  1. Can understand the problem formulation and the representation of mathematical programming.
  2. Can understand the basic idea of linear mathematical programming and can solve the problems by using graphical approach and the simplex method.
  3. Can understand the basic idea of nonlinear mathematical programming and can manage to obtain the analytic solutions and the numerical solutions.
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 Excel solvers;

Mid-term report 		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 report Review of the whole course 190minutes
Total. - - 2660minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Mid-term report Final report Total.
1. 20% 10% 30%
2. 20% 20% 40%
3. 30% 30%
Total. 40% 60% -
Evaluation method and criteria
Mid-term report : 40%, Final report: 60%

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.
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
Desirable to have basic knowledge on linear algebra and elementary calculus.
Office hours and How to contact professors for questions
  • 火曜日 12:30 -- 13:00
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates a basic self-management skills
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
More than one class is interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
Applicable 沖電気工業株式会社で２年間ネットワーク制御の解析と設計を行ったため、その研究開発の経験と内容を一部授業に反映している
Education related SDGs:the Sustainable Development Goals
  • 4.QUALITY EDUCATION
  • 5.GENDER EQUALITY
  • 7.AFFORDABLE AND CLEAN ENERGY
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
  • 12.RESPONSIBLE CONSUMPTION & PRODUCTION
  • 13.CLIMATE ACTION
  • 16.PEACE, JUSTICE AND STRONG INSTITUTIONS
  • 17.PARTNERSHIPS FOR THE GOALS
Last modified : Fri Mar 18 22:31:11 JST 2022