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10-801: Advanced Optimization and Randomized Methods

10-801: Advanced Optimization and Randomized Methods Lecture 2: Convex functions (Jan 15, 2014). Lecturer: Suvrit Sra Scribes: Avinava Dubey, Ahmed Hefny Addr: Carnegie Mellon University, Spring 2014. Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications. They may be distributed outside this class only with the permission of the Instructor. Review The lecture began with a review of convexity in metric spaces, a topic that we could not cover fully in Lecture 1. Definition A metric space (X , d) is called complete if any Cauchy sequence within the space converges to a point in the space.

10-801: Advanced Optimization and Randomized Methods Lecture 2: Convex functions (Jan 15, 2014) Lecturer: Suvrit Sra Scribes: Avinava Dubey, Ahmed Hefny Addr: Carnegie Mellon University, Spring 2014 Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal publications.They may be distributed

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