Introduction to Convexity - 625.694

Convexity is a simple mathematical concept that has become central in a diverse range of applications in engineering, science, and business applications. Our main focus, from the applications perspective, will be the use of convexity within optimization problems, where convexity plays a key role in identifying the “easy” problems from the “hard” ones. The course will have an equal emphasis on expositing the rich mathematical structure of the field itself (properties of convex sets, convex functions, polarity/duality, subdifferential calculus, polyhedral theory, sublinearity), and demonstrating how these ideas can be used to model and solve optimization problems.The course requires basic familiarity with concepts like sequences, convergence and limits at the level of a rigorous multivariate calculus course (a course in real analysis such as EN.625.601, will be more than sufficient, but only the most basic ideas from real analysis are needed; a formal course is not required). The course also needs background in basic linear algebra at the level of EN.625.252 (EN.625.609 will be more than sufficient).Prerequisites: Multivariable calculus, linear algebra