Optimization Algorithms

Fundamental theory for solving continuous optimization problems with provable efficiency guarantees. Coverage of both canonical optimization methods and techniques, e.g. gradient descent, mirror descent, stochastic methods, acceleration, higher-order methods, etc. and canonical optimization problems, critical point computation for non-convex functions, smooth-convex function minimization, regression, linear programming, etc. Focus on provable rates for solving broad classes of prevalent problems including both classic problems and those motivated by large-scale computational concerns. Discussion of computational ramifications, fundamental information-theoretic limits, and problem structure. Prerequisite: linear algebra, multivariable calculus, probability, and proofs.