Operations Research (3): Theory
Explore advanced theoretical concepts in linear, integer, and nonlinear programming for operations research.
Explore advanced theoretical concepts in linear, integer, and nonlinear programming for operations research.
This advanced-level course delves into the mathematical properties of linear, integer, and nonlinear programs in operations research. Students will study advanced topics such as duality theory, sensitivity analysis, network flows, convex analysis, and Lagrangian relaxation. The course emphasizes theoretical foundations and their practical applications in solving complex optimization problems. Through lectures, quizzes, and case studies, learners will develop a deep understanding of the mathematical underpinnings of operations research techniques.
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What you'll learn
Master the theoretical foundations of linear, integer, and nonlinear programming
Understand and apply duality theory in various optimization contexts
Analyze sensitivity and post-optimality in linear programming
Explore network flow problems and their unique properties
Apply convex analysis to nonlinear optimization problems
Utilize Lagrangian relaxation and KKT conditions for constrained optimization
Skills you'll gain
This course includes:
11.42 Hours PreRecorded video
8 assignments
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There are 8 modules in this course
This advanced course in Operations Research theory provides a deep dive into the mathematical foundations of optimization techniques. The curriculum covers a wide range of topics, starting with a matrix-based approach to the simplex method. It then explores duality theory, sensitivity analysis, and the dual simplex method. The course delves into network flow problems and their special properties, followed by convex analysis and its applications in nonlinear programming. Advanced topics include Lagrangian duality, the Karush-Kuhn-Tucker (KKT) conditions, and their applications in constrained optimization. The course concludes with case studies on linear regression and support vector machines, demonstrating the practical applications of these theoretical concepts in machine learning and data analysis.
Course Overview
Module 1 · 1 Hours to complete
Duality
Module 2 · 2 Hours to complete
Sensitivity Analysis and Dual Simplex Method
Module 3 · 1 Hours to complete
Network Flow
Module 4 · 1 Hours to complete
Convex Analysis
Module 5 · 2 Hours to complete
Lagrangian Duality and the KKT condition
Module 6 · 2 Hours to complete
Case Study
Module 7 · 1 Hours to complete
Course Summary and Future Learning Directions
Module 8 · 48 Minutes to complete
Fee Structure
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Instructor
Leading Authority in Nephrology and Toxicology at National Taiwan University.
Dr. Chih-Kang Chiang is an expert in internal medicine, nephrology, toxicology, and food safety risk analysis. He received his Ph.D. in 2006 from the Graduate Institute of Toxicology at National Taiwan University. In 2005, he became a clinical lecturer in the Department of Internal Medicine at National Taiwan University and was promoted to clinical assistant professor in 2007 and clinical associate professor in 2012. He has served as an associate professor since 2014 and was promoted to full professor in 2018 at the Graduate Institute of Toxicology, National Taiwan University. A notable scholar in nephrology and toxicology, Dr. Chiang has published over a hundred peer-reviewed articles throughout his career.
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78 ratings
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