ORIE 6365

Continuous Optimization: Algorithms and Complexity

Course Description

Course information provided by the 2025-2026 Catalog.

Graduate course on the theory and algorithms of continuous optimization. Prepares students for research in optimization theory and for developing advanced methods for applications in operations research, machine learning, and related domains. Topics: convexity, smooth and non-smooth problems, duality. Ellipsoid and subgradient methods. Mirror descent and the geometry of optimization problems. Accelerated optimal methods, lower complexity bounds and resisting oracles. Composite problems. Stochastic and large-scale optimization, variance reduction techniques. Second-order algorithms: Newton, quasi-Newton, and interior-point methods. Applications will be drawn from machine learning, semidefinite programming, and large-scale graph optimization.

Prerequisites multivariate calculus and linear algebra.

Last 4 Terms Offered (None)

Learning Outcomes

• Identify and classify continuous optimization problems based on their structure
• Design and implement efficient algorithms to solve different classes of optimization problems
• Analyze and compare convergence rates and complexity bounds of optimization methods

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