This series of video lectures features the theory of convex analysis in finite dimensions and applications to optimization. The lectures are based on my recently published book “An Easy Path to Convex Analysis and Applications” (co-authored with Boris Mordukhovich) published by the Morgan & Claypool in 2013. Important topics of convex analysis such as subgradients, subdifferential calculus rules, Fenchel conjugate, differentiability of convex functions, and applications are presented with detailed proofs.
During this video project, Dr. Mau Nam Nguyen was partly supported by the National Science Foundation and the Faculty Development Program at Portland State University.
Chapter 1: Convex Sets and Functions
Chapter 2: Subdifferential Calculus
Chapter 3: Other Consequences of Convexity
Chapter 4: Applications to Optimization
Chapter 5: Convex Numerical Algorithms