ORIE 6367

Advanced Algorithms in Continuous Optimization

Course Description

Course information provided by the 2026-2027 Catalog.

The field of continuous optimization lies at the intersection of applied mathematics, operations research, and a wide range of scientific and engineering applications. In recent years, the rapid growth of data-driven technologies and large-scale computational models has led to intense research activity in the development and analysis of efficient optimization algorithms. Significant progress has been made in convex optimization, with mature theory and scalable algorithms now available. However, many modern applications arising in machine learning, signal and image processing, data science, and engineering design lead to inherently nonconvex optimization problems. For such problems, algorithmic design is considerably more challenging, and theoretical understanding is far less complete. This course focuses on algorithms for continuous optimization, with an emphasis on both convex and nonconvex settings. We will study a mixture of classical foundational methods and recent algorithmic developments that are widely used in contemporary applications.

Prerequisites ORIE 6300 or equivalent coursework or any other advanced optimization course.

Last 4 Terms Offered (None)

Learning Outcomes

• Students will demonstrate a rigorous understanding of core principles in continuous optimization, specifically in first-order methods, and will be able to analyze convergence properties in both convex and nonconvex settings.
• Students will be able to design, adapt, and critically evaluate optimization algorithms for large-scale problems, with particular attention to computational efficiency, scalability, and the role of problem structure.
• Students will be able to formulate optimization models arising in modern applications (e.g., machine learning, signal processing, and data science), select appropriate algorithms, and critically assess their practical performance and theoretical guarantees.

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