2020 Advanced Mathematical Programming

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Academic unit or major
Graduate major in Industrial Engineering and Economics
Matsui Tomomi 
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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.


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 in the first half and then assign some exercise problems in the last half.

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


None required

Reference books, course materials, etc.

Course materials will be provided as needed.

Assessment criteria and methods

Evaluation based on reports and exams

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.

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