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.
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.
Linear programming (simplex method, duality theorem), Network optimization, PERT, Integer programming (combinatorial optimization), Nonlinear programming
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
A fill-in-the-blank textbook is used. Each student fills in them in class.
|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|
Wakaha Ogata, "Mathematical Programming" Ohmsha.
The above target is evaluated by final exam
Students must have acquired the basic knowledge of linear algebra and calculus.