Unconstrained Nonlinear Optimization Fundamentals
Master the principles and algorithms of unconstrained nonlinear optimization, including Newton's method and descent techniques.
Master the principles and algorithms of unconstrained nonlinear optimization, including Newton's method and descent techniques.
Dive into the world of unconstrained nonlinear optimization with this comprehensive course. From problem formulation to advanced solution techniques, you'll gain a solid foundation in optimization theory and practice. The course covers essential topics such as objective function properties, optimality conditions, Newton's method, and descent algorithms. You'll learn how to formulate and transform optimization problems, understand the mathematical properties crucial for optimization, and apply various solution methods. With a focus on both theoretical understanding and practical application, this course is ideal for students and professionals in mathematics, computer science, engineering, and related fields looking to enhance their optimization skills. Optional Python programming exercises provide hands-on experience in implementing optimization algorithms.
Instructors:
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What you'll learn
Formulate and transform unconstrained nonlinear optimization problems
Analyze the mathematical properties of objective functions in optimization contexts
Apply sufficient and necessary conditions for optimal solutions
Implement and interpret Newton's method for solving nonlinear equations
Adapt Newton's method for optimization problems
Understand and apply various descent methods in optimization
Skills you'll gain
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Graded assignments, exams
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Module Description
This course provides a comprehensive introduction to unconstrained nonlinear optimization, covering both theoretical foundations and practical algorithms. The curriculum is structured into six main sections: 1) Formulation: teaching how to formulate, transform, and characterize optimization problems through examples; 2) Objective function: reviewing the mathematical properties of objective functions crucial for optimization; 3) Optimality conditions: exploring sufficient and necessary conditions for optimal solutions; 4) Solving equations with Newton's method: a review of this fundamental technique; 5) Newton's local method in optimization: adapting and interpreting Newton's method for optimization problems; 6) Descent methods: introducing the family of descent methods and their connection to Newton's method. Throughout the course, students will learn to apply these concepts to real-world optimization problems, with optional Python programming exercises to implement the algorithms discussed. The course emphasizes both theoretical understanding and practical application, preparing students for advanced study or application of optimization techniques in various fields.
Fee Structure
Instructor
2 Courses
Pioneer in Radio Astronomy and Interferometry
Oleg Smirnov is a Distinguished Professor holding the SARAO Research Chair in Radio Astronomy Techniques and Technologies at Rhodes University while heading the Radio Astronomy Research Group at the South African Radio Astronomy Observatory. After receiving his Ph.D. in Astronomy & Astrophysics from the Russian Academy of Sciences in 1998, he began his career at ASTRON in the Netherlands. His research focuses on calibration and imaging techniques for radio interferometry, developing sophisticated algorithms and software for next-generation radio telescopes. Under his leadership, the Radio Astronomy Research Group has produced groundbreaking MeerKAT telescope images and established itself as a leading force in bridging radio astronomy with engineering. His work spans radio interferometry, calibration techniques, and software development for astronomical applications. He leads an international team of researchers and doctoral students, contributing to the development of the Square Kilometre Array (SKA) project while advancing cloud-based technologies for radio interferometry data processing.
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