This course, Convex Optimization I, focuses on identifying and addressing convex optimization problems prevalent in engineering disciplines. Key topics include:
Prerequisites include a solid understanding of linear algebra. While experience in numerical computing and optimization is advantageous, the course will maintain a straightforward approach to engineering applications.
This module introduces the foundational concepts of convex optimization, providing examples and techniques for solving optimization problems. Key areas of focus include:
This module features a guest lecture by Jacob Mattingley, who discusses various concepts of convex sets and operations preserving convexity. Topics include:
This module centers on logistics and the critical properties of convex functions. It includes:
This module delves into vector composition and its implications in convex optimization. The focus areas include:
This module focuses on optimal and locally optimal points within convex optimization problems. Key topics include:
This module introduces generalized linear-fractional programming along with related concepts. Topics covered include:
This module covers generalized inequality constraints in optimization problems. It focuses on:
This module introduces the Lagrangian method and its significance in convex optimization. Key topics include:
This module elaborates on complementary slackness and Karush-Kuhn-Tucker (KKT) conditions relevant to convex problems. It includes:
This module focuses on the applications of convex optimization in various fields. It covers:
This module dives into statistical estimation, covering essential concepts and methodologies. Key topics include:
This module continues the discussion on experiment design with a focus on geometric problems. It addresses:
This module continues the examination of linear discrimination, emphasizing robust techniques and applications. It includes:
This module continues the discussion on LU factorization, exploring advanced concepts and methods. Key topics include:
This module explores the algorithmic aspects of convex optimization, focusing on unconstrained minimization techniques. It covers:
This module continues the exploration of unconstrained minimization, introducing self-concordance and its significance. Key points include:
This module continues the discussion on Newton's method, focusing on its applications in convex optimization. Topics include:
This module focuses on logarithmic barriers and their implications for convex optimization. Key areas include:
This module concludes the course with a review of interior-point methods and their complexities. It includes: