Understand convex sets, functions, and optimization algorithms with hands-on examples and expert instruction.
Sub Category
- Data Science
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Objectives
- Understand what convex sets and convex functions are, and why they matter in optimization.
- Explore how convexity helps solve real-world problems like shortest paths, image processing, and machine learning.
- Learn the geometry and structure of high-dimensional spaces using inner-product spaces.
- Discover how to analyze and work with functions that aren’t smooth using subgradients.
- Study key optimization algorithms like the subgradient method and forward-backward splitting.
- Key algorithms - subgradient method, forward-backward splitting, and accelerated techniques for solving large-scale problem
- Learn about accelerated methods that improve the speed of convergence.
- Subdifferentials & Epigraphs: Learn how to analyze non-differentiable functions using subgradients and epigraphs, essential tools in nonsmooth optimization.
- Dive into duality theory to understand the relationship between primal and dual optimization problems.
- Duality Theory: Explore the powerful framework of Fenchel, Lagrange, and strong duality, and how dual problems provide deep insights into primal formulations.
- Applications: Apply convex optimization to real-world problems such as shortest-path computations, support vector machines, and signal/image processing.
- Gain the skills to model, analyze, and solve large-scale convex optimization problems in practical settings.
Pre Requisites
- Mathematical Maturity: Comfort with abstract mathematical reasoning and notation.
- Linear Algebra: Familiarity with vectors, matrices, inner-product spaces, and basic operations.
- Calculus: Understanding of differentiation, continuity, and basic function properties.
FAQ
- Q. How long do I have access to the course materials?
- A. You can view and review the lecture materials indefinitely, like an on-demand channel.
- Q. Can I take my courses with me wherever I go?
- A. Definitely! If you have an internet connection, courses on Udemy are available on any device at any time. If you don't have an internet connection, some instructors also let their students download course lectures. That's up to the instructor though, so make sure you get on their good side!
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