## Course Title : System Optimization

Code 60660 3rd year 2nd term 2 No Restriction Lecture E. Furutani

### Course Description

The course deals with mathematical methods of system optimization for linear programming and nonlinear programming problems. It covers such topics as the formulation of optimization problem, solution and analysis methods of linear programming problems, optimality conditions and solution methods of nonlinear programming problems.

The assignments are only for understanding; the rating will be based on an exam.

### Course Goals

To understand fundamentals of linear programming and nonlinear programming: the simplex method, duality, locally and globally optimal solution, convex space and convex functions, optimality conditions for nonlinear programming problems, and basic solution methods.

### Course Topics

Theme Class number of times Description
Optimization problems 1 optimality, overview and classification of optimization problems, mathematical preliminary
Linear programming and simplex method 7-8 definition of linear programming problems, standard form, simplex method and simplex tableau, duality, dual problems, duality theorem, dual simplex method, and sensitivity analysis
Nonlinear programming problems 1 definition of nonlinear programming problems, locally optimal solution and globally optimal solution, convex space and convex function, mathematical preliminary
Solution methods for nonlinear programming problems without constraints 2-3 optimality conditions for nonlinear programming problems without constraints, steepest descent method, conjugate gradient method, Newton method, and quasi-Newton method
Solution methods for nonlinear programming problems with constraints 3-4 optimality conditions for nonlinear programming problems with constraints, Lagrange function, duality, saddle point theorem, penalty function method, multiplier method, and sequential quadratic programming method

### Textbook

H. Tamaki (ed.): System Optimization (in Japanese), Ohm-sha, 2005 .

### Textbook(supplemental)

M. Fukushima: Introduction to Mathematical Programming (in Japanese), Asakura, 1996 .

### Prerequisite(s)

linear algebra and analytics

### Web Sites

http://turbine.kuee.kyoto-u.ac.jp/~furutani/system-optimization/