ORIE 3320

Optimization for AI

Course Description

Course information provided by the 2025-2026 Catalog.

This course introduces the theory, algorithms, and applications of nonlinear optimization, which is at the core of many fundamental algorithmic challenges in AI, such as the training of models like deep neural nets and transformers, and is used at massive scales. We will study unconstrained and constrained optimization problems, focusing on convex and nonconvex settings. Topics include optimality conditions, convexity, gradient-based and Proximal-type methods, second-order methods, line-search strategies, and duality theory. Emphasis will be placed on both the mathematical foundations and the practical implementation of algorithms.

Prerequisites MATH 1910, MATH 2940.

Last 4 Terms Offered (None)

Learning Outcomes

• Formulate and analyze unconstrained and constrained nonlinear optimization problems, identifying convexity, feasibility, and optimality conditions.
• Apply and implement first- and second-order optimization algorithms, and evaluate their convergence behavior in practice.
• Model and solve real-world applications using nonlinear optimization techniques in areas such as machine learning, engineering, and operations research.

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