### 2020　Advanced Mathematical Programming

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Academic unit or major
Graduate major in Industrial Engineering and Economics
Instructor(s)
Matsui Tomomi
Course component(s)
Lecture    (ZOOM)
Day/Period(Room No.)
Tue7-8(Zoom)  Fri7-8(Zoom)
Group
-
Course number
IEE.A432
Credits
2
Academic year
2020
Offered quarter
4Q
Syllabus updated
2020/12/4
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

Many of mathematical problems arising in the areas of economics and industrial engineering can be formulated as discrete optimization problems. In this lecture, we pick up integer programming problems, network programming problems, and combinatorial optimization problems. We explain the mathematical structures of the solution sets of the problems, and connection with combinatorics. We also review various algorithms for discrete optimization problems.
The objective is to let students learn skills which is necessary to solve discrete optimization problems.

### Student learning outcomes

By the end of this course, students will be able to:
・Understand fundamental properties of discrete optimization problems.
・Understand fundamental properties of the branch and bound method.
・Understand fundamental properties of typical approximation algorithms.
・Understand fundamental properties of typical heuristics.

### Keywords

discrete optimization problem, integer programming problem, combinatorial optimization problem, the branch and bound method, approximation algorithms, heuristics.

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

In each class we give a lecture and assign some exercise problems if needed.

### Course schedule/Required learning

Course schedule Required learning
Class 1 fundamental properties of discrete optimization problems. understand the contents of each class
Class 2 algorithm and complexity
Class 3 overview of linear programming and the duality theorem
Class 4 relaxation method
Class 5 Lagrange relaxation and subgradient method
Class 6 enumerative method
Class 7 linear relaxation problem
Class 8 branch and bounds method
Class 9 dual simplex method
Class 10 additive lower bounds
Class 11 approximation algorithm
Class 12 randomized algorithm
Class 13 heuristics
Class 14 introduction to complexity theory
Class 15 summary

### Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

None required

### Reference books, course materials, etc.

Course materials will be provided as needed.

### Assessment criteria and methods

Evaluation based on reports

### Related courses

• IEE.B433 ： Advanced Topics in Mathematical Economics

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites are necessary, but enrollment in related courses is desirable. 