Course title
L09866003
Mathematical Programming

 igarashi harukazu Click to show questionnaire result at 2018
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 three solution methods for nonlinear programming problems. The latter methods are “descent method”, “conjugate gradient method” and “Newton method”. But only optimization problems without constraints are covered by this course. 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, integer programming problems and nonlinear programming problems. Read this syllabus and Ref. (1), pp.1-6 to understand what mathematical programming is. 100minutes
2. Examples of linear programming problems and their solutions : Graphical method and algebraic method Read Ref. (1), pp.7-11 and review how to draw a region given by linear inequalities. 100minutes
3. 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. 200minutes
4. Theory of simplex methods : Canonical form, basis and simplex tableau Read Ref. (1), pp.21-32. Review matrix calculation. 100minutes
5. Algorithm of simplex methods : Example of production planning problems Review the content of the 4th lecture. 100minutes
6. The dual problem of linear programming and duality Read Ref. (1), pp. 58-64. 100minutes
7. Midterm exam, Q&A Review the contents of the 1st to the 6th lecture. 800minutes
8. 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
9. Descent methods Read Ref. (1), pp.168-171 and the slides of the 10th lecture. 100minutes
10. Theory of conjugate gradient methods Read Ref. (1), pp.172-176. 100minutes
11. Algorithms of conjugate gradient methods and examples of the application. Read Ref. (1), pp.177-178 and the slides of the 12th lecture. 100minutes
12. Newton method Read Ref. (1), pp.179-181 and Ref. (2), pp.91-93. 100minutes
13. Lagrange’s method of indeterminate multipliers Read Ref. (2), pp.60-74. 100minutes
14. Final exam, Q&A Review the contents of the 7th to the 14th lecture. You are expected to solve concrete problems if the general formula or algorithm is presented. 550minutes
Total. - - 2650minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Midterm exam Final exam Total.
1. 10% 0% 10%
2. 30% 0% 30%
3. 0% 60% 60%
Total. 40% 60% -
Evaluation method and criteria
Grading: Midterm exam (40%) and fiinal exam (60%). 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.
Relation to the environment
Non-environment-related course
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 applicatable
N/A N/A
Last modified : Thu Mar 21 15:08:51 JST 2019