Convex Optimization, Spring 2017, Notes

Notes 1, introduction to optimization and model problems

Notes 2, convex sets, separating hyperplanes, the closest point problem
Notes 3, introduction to duality
Notes 4, convex functions
Notes 5, a second look at duality (Fenchel)

Unconstrained Optimization
Notes 6, basic theory of unconstrained smooth optimization
Notes 7, gradient descent
Notes 8, Newton’s method
Notes 9, quasi-Newton methods
Notes 10, accelerated first-order methods

Constrained Optimization
Notes 11, geometric optimality conditions
Notes 12, KKT conditions
Notes 13, Lagrange duality
Notes 14, dual examples
Notes 15, basic algorithms for constrained optimization
Notes 16, ADMM

Notes 17 [blackboard], robust programming, SDPs, statistical estimation, multi-criterion optimization
Notes 18, convex relaxations
Notes 19, L1 minimization for sparse recovery

Non-smooth Optimization
Notes 20, subgradients and basic theory
Notes 21, subgradient method
Notes 22, proximal methods
Notes 23, proximal gradient method
Notes 24, non-smooth quiz