Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2022Year School of Informatics and Data Science KA118001 Specialized Education 数理計画法 スウリケイカクホウ Mathematical Programming NISHIZAKI ICHIROU ニシザキ　イチロウ Higashi-Hiroshima 2nd-Year,  First Semester,  1Term (1T) Weds3-4,Fri1-2：ENG 220 Lecture LectureThere is a possibility that lectures are  conducted face-to-face. 2.0 J : Japanese 2 : Undergraduate Low-Intermediate 25 : Science and Technology 11 : Electrical, Systems, and Control Engineering Students enrolled in and before 2020 Linear programming, simplex method, two-phase simplex method, dual simplex method, integer programming, branch and bound method, nonlinear programming, Kuhn-Tucker conditions, Lagrangian function, descent method Informatics and Data Science Program（Comprehensive Abilities）・I2. Ability to provide the most appropriate system solution to a cross-sectional problem in the diversified and complicated information society based on the many forms of cutting edge information technology. Explanation and practice of mathematical programming theory which is one of most basic systems optimization methods lesson1 Linear programming: Summary of mathematical programminglesson2 Linear programming: Algebraic computations and definitions of linear programming problemslesson3 Linear programming: Theory and algorithm of simplex methodlesson4 Linear programming: Theory and algorithm of two-phase methodlesson5 Linear programming: Theory and algorithm of dual simplex methodlesson6 Integer programming: Modelling based on integer programming probmeslesson7 Integer programming: Basic framework of integer programminglesson8 Integer programming: Theory and algorithm of branch and bound methodlesson9 Practices of linear and integer programminglesson10 Intermediate exam (linear and integer programming)lesson11 Nonlinear programming: Nonlinear programming problems and their conceptual foundationslesson12 Nonlinear programming: Optimality condition for constrained and non-constrained optimization problemslesson13 Nonlinear programming: Algorithm for solving non-constrained optimization problemslesson14 Nonlinear programming: Algorithm for solving nonlinear programming problemslesson15 Practices of nonlinear programmingIntermediate and final examinations, assignments Textbook: Masatoshi Sakawa and Ichiro Nishizaki, ``Introduction to Mathematical Programming'', Morikita Publishing Co., Ltd. (in Japanese) Textbook, PC, projector 1. Understand examples of mathematical programming problems in the real world2. Learn basic concepts and terms about linear programming problems3. Understand assumptions, the principle and the algorithm of simplex method by applying it to examples4. Understand the principle and the algorithm of two-phase simplex method by applying it to examples5. Understand the principle and the algorithm of dual simplex method by applying it to examples6. Understand the formulation process of actual optimization problems as integer programming problems7. Learn basic concepts and terms about integer programming problems8. Understand the principle and the algorithm of branch and bound method by applying it to examples9. Master the optimization methods for linear and integer programming problems by exercises10. Understand the optimization methods for linear and integer programming problems11. Understand the formulation process of actual optimization problems as nonlinear programming problems12. Understand Kuhn-Tucker conditions and Lagrangian function13. Understand the principle and the algorithm of descent method and Newton method by applying them to examples14. Understand the principle and the algorithm of penalty method and generalized reduced gradient method by applying them to examples15. Master the optimization methods for nonlinear programming problems by exercises 1. Watch all videos and submit assignments. (Attendance at all classes is necessary as a rule.)2. An elementary knowledge of mathematics is necessary. Intermediate and final examinations, and assignments, the passing mark is 60. Please fill in the class improvement questionnaire which is carried out on all classes.Instructors will reflect on your feedback and utilize the information for improving their teaching.
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