Convex optimization is a cornerstone of modern applied mathematics, underpinning a wide range of technologies from machine learning and artificial intelligence to signal processing, control systems, and operations research. This course offers a deep and structured exploration of large-scale convex optimization, tailored for learners who seek both theoretical rigor and practical insight.
Through 55 carefully crafted video lectures, this course guides you from the foundational concepts of convex sets and functions to advanced algorithmic techniques for solving high-dimensional optimization problems.
It is designed to be accessible to motivated learners while maintaining the depth expected in graduate-level education. This course:
- Offers a structured deep dive into large-scale convex optimization, balancing theory and algorithmic practice.
- Introduces core concepts: convex sets, convex functions, and their properties—essential for high-dimensional optimization.
- Begins with real-world applications: shortest-path problems, signal/image processing, and support vector machines.
- Covers mathematical foundations: inner-product spaces, convex geometry, convexity-preserving operations, differentiability, lower semicontinuity, and closedness.
- Focuses on algorithmic techniques: Subgradient method: convergence, boundedness, and implementation; and Forward-backward splitting and accelerated variants for composite problems.
- Explores duality theory: Primal-dual relationships; Perturbation and infimal value functions; Fenchel and Lagrange duality frameworks.
- Equips learners to analyze, solve, and implement convex optimization methods in practical and research contexts.
By the end of this course, you will:
- Understand the theoretical underpinnings of convex optimization
- Be able to formulate and solve large-scale convex problems
- Implement key algorithms for optimization in practical settings
- Apply convex optimization to real-world problems in engineering and data science
- Be prepared for advanced studies or research in optimization and applied mathematics
