Course title
L09866003
Mathematical Programming

 igarashi harukazu Click to show questionnaire result at 2019
Course description
Mathematical programming (MP) plays a key role in system optimization and planning. This course presents the simplex method for linear programming problems and two basic solution methods for nonlinear programming problems. The latter two methods are "descent method" and " Lagrange's method of indeterminate multipliers ". Theoretical frame works of solution and concrete algorithms are explained.
Purpose of class
To learn basic solutions for linear programming problems and nonlinear programming problems and apply the solutions to problems in specific cases.
Goals and objectives
  1. To understand that practical planning problems in the real world can be formulated as mathematical planning problems and formulate some simple problems by yourself.
  2. To explain the principles of the simplex method and solve simple linear programming problems using this method.
  3. To understand typical optimization methods for nonlinear programming problems and solve simple nonlinear programming problems using these methods.
Language
Japanese
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. What is Mathematical programming? : Examples of linear programming problems and Graphical method. Read this syllabus and Ref. (1), pp. 1-11 to understand what mathematical programming is. 100minutes
Review how to draw a region given by linear inequalities.
2. Standard linear programming problems and basic technical terms : Production planning problems, diet problems and standard form. Read Ref. (1), pp. 12-20. Review matrix representation and sigma notation. 100minutes
3. Theory of simplex methods : Canonical form, basis and simplex tableau Read Ref. (1), pp.21-32. Review matrix calculation. 200minutes
4. Algorithm of simplex methods : Example of production planning problems Review the content of the 3rd lecture. 200minutes
5. Examples of nonlinear programming problems and mathematical preliminaries : Gradient vector Read Ref. (1), pp.165-167, Ref. (2), pp.79-85 and Ref. (3), pp.59-68. 100minutes
6. Descent methods and Lagrange's method of indeterminate multiplier Read Ref. (1), pp. 168-171 and the slides of the 10th lecture. Read Ref. (2), pp.60-74. 200minutes
7. Final exam, Q&A Review the contents of the 1th to the 6th lecture. You are expected to solve concrete problems if the general formula or algorithm is presented. 600minutes
Total. - - 1500minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Reports Final exam Total.
1. 20% 10% 30%
2. 20% 10% 30%
3. 20% 20% 40%
Total. 60% 40% -
Evaluation method and criteria
Grading: Reports (60%) and flinal exam (40%). Over 60% in total is acceptable.
Textbooks and reference materials
Recommending

(1) M. Sakawa, “Basis of mathematical programming methods,” Morikitashuppan (in Japanese).
(2) K. Kanatani, “Easy-to-understand mathematics of optimization,” Kyoritushuppan (in Japanese).
(3) N. Kato, “Mathematical Programming,” Coronasha, (in Japanese).
Prerequisites
Prerequisites : Understanding the contents of “Data Structure and Algorithms 2”(L0694500) and having a basic knowledge of calculus and linear algebras. Mathematical skills to deal with equations are also required.
Office hours and How to contact professors for questions
  • Anytime except lecture hours at my office (Room no.14M32 or 14K30). E-mail contact is also available to ask questions.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
N/A
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals
  • 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
  • 12.RESPONSIBLE CONSUMPTION & PRODUCTION
Last modified : Sun Mar 21 15:10:24 JST 2021