2019 Mathematical Programming

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Academic unit or major
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
Academic year
2019
Offered quarter
3Q
Syllabus updated
2019/8/20
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.

Reference books, course materials, etc.

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.

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