Continuous Optimization: Algorithms and Complexity

3.0 credits · Graduate

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.