System Optimization

Numbering Code U-ENG26 36066 LJ72 Year/Term 2021 ・ Second semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Tue.3
Instructor name SAKAMOTO TAKUYA (Graduate School of Engineering Associate Professor)
Outline and Purpose of the Course 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.
Course Goals To understand fundamentals of linear programming and nonlinear programming: the simplex method, duality, locally and globally optimal solutions, convex space and convex functions, optimality conditions and basic solution methods for nonlinear programming problems.
Schedule and Contents Optimization problems,1time,optimality, overview and classification of optimization problems, mathematical preliminary
Linear programming and simplex method,7-8times,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,1time,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,2-3times,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,2-3times,optimality conditions for nonlinear programming problems with constraints, Lagrange function, Lagrange multiplier method, duality, saddle point theorem, penalty function method, multiplier method, and sequential quadratic programming method
Review,1time,The level of understanding on this lecture will be confirmed.
Evaluation Methods and Policy The assignments are only for understanding; the rating will be based on an exam.
Course Requirements linear algebra and analytics
Study outside of Class (preparation and review) Will be discussed as needed.
Textbooks Textbooks/References H. Tamaki (ed.): System Optimization (in Japanese), Ohm-sha, 2005 isbn{}{4274201627}.
References, etc. M. Fukushima: Introduction to Mathematical Programming (in Japanese), Asakura, 1996 isbn{}{9784254209754} isbn{}{9784254280043}.
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