Course Title : Linear Programming

Code 90690
Course Year 1st year
Term
Class day & Period
Location
Credits 2
Restriction No Restriction
Lecture Form(s) Lecture
Language Japanese
Instructor

Course Description

Lectures on modeling and algorithms of mathematical optimization, with main focus on linear programming, which is the most fundamental subject in system optimization.

Grading

Based on the score of the term examination.

Course Goals

To learn the basic ideas of formulating optimization models, and to understand theoretical properties and solution methods of linear programming.

Course Topics

Theme Class number of times Description
Introduction to Mathematical Optimizaiton 1 Introduction to Mathematical Optimization. Reviews of some mathematics for linear programming, in particular, linear algebras.
Mathematical Programming Models 4 Representative mathematical programming models such as linear programming models, network programming models, noninear programming models, and combinatorial programming models, with simple illustrative examples.
Linear Programming and Basic Solutions 2 Formulation of linear programs in the standard form, and basic concepts of basic solutions, basic feasible solutions, and optimal basic solutions.
Simplex Method 3 Basic ideas and concrete procedures of the simplex method that is a classical method for linear programming. Topics include two-stage linear programming, variables with upper bounds, and network simplex methods.
Duality and Sensitivity Analysis 3 Duality as an important theory in linear programming, and sensitivity analysis as a useful technique in decision making.
Interior Point Methods 1 Interior point methods as polynomial-time algorithms in linear programming.
Review and Summary 1 Review and Summary. Confirmation of achievement level.

Textbook

Fukushima, M.: Introduction to Mathematical Programming: New Edition (in Japanese), Asakura Shoten .

Textbook(supplemental)

Prerequisite(s)

Web Sites

Additional Information