### 2018　Mathematical Programming

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Undergraduate major in Information and Communications Engineering
Instructor(s)
Koike Yasuharu
Course component(s)
Lecture
Day/Period(Room No.)
Mon1-2(W631)  Thr1-2(W631)
Group
-
Course number
ICT.M310
Credits
2
2018
Offered quarter
3Q
Syllabus updated
2018/4/11
Lecture notes updated
-
Language used
Japanese
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### Course description and aims

Mathematical programming is a study on methods to decide optimal parameters under given constraints, which help to solve various problems.
This course introduces varied approaches according to the type of given problem.

### Student learning outcomes

At the end of this course, students will be able to:
1) solve fundamental optimization problems.
2) apply the theory of basic mathematical programming to practical problems.

### Keywords

Linear programming (simplex method, duality theorem), Network optimization, PERT, Integer programming (combinatorial optimization), Nonlinear programming

### Competencies that will be developed

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

### Class flow

A fill-in-the-blank textbook is used. Each student fills in them in class.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Introduction to mathematical programming After each class, review what you learnt and do exercises in the textbook.
Class 2 Linear programming I : Standard form and geometrical solution Understand of Standard form and geometrical solution
Class 3 Linear programming II : Simplex method Understand of Simplex method
Class 4 Linear programming III : Two-phase simplex method Understand of Two-phase simplex method
Class 5 Linear programming IV : Duality theorem Understand of Duality theorem
Class 6 Network optimization I : Shortest path problem Understand of Shortest path problem
Class 7 Network optimization II : Maximum flow problem Understand of Maximum flow problem
Class 8 Network optimization III : Minimum cost flow problem Understand of Minimum cost flow problem
Class 9 Network optimization I : Program evaluation and review technique (PERT) Understand of Program evaluation and review technique (PERT)
Class 10 Combinatorial optimization I : Greedy method and branch-and-bound method Understand of Greedy method and branch-and-bound method
Class 11 Combinatorial optimization II : Dynamic programming and heuristi Understand of Dynamic programming and heuristi
Class 12 Nonlinear programming I : unconstrained optimization (steepest descent method) Understand of unconstrained optimization (steepest descent method)
Class 13 Nonlinear programming II : unconstrained optimization (Newton method) Understand of unconstrained optimization (Newton method)
Class 14 Nonlinear programming III: Constrained optimization Understand of Constrained optimization
Class 15 Review of important items all over the course

### Textbook(s)

Wakaha Ogata, "Mathematical Programming" Ohmsha.

None required.

### Assessment criteria and methods

The above target is evaluated by final exam

### Related courses

• ZUS.F201 ： Numerical Analysis
• ZUS.F301 ： Foundations of Functional Analysis

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

Students must have acquired the basic knowledge of linear algebra and calculus.