Lec 1 (Jan 7): Introduction to optimization and several types of functions
Lec 2 (Jan 9): Univariate optimization: optimality conditions and Newton's method
Lec 3 (Jan 14): Analysis of Newton’s method
Lec 4 (Jan 16): Linear algebra and convergence in metric space
Lec 5 (Jan 21): Continuous functions and coercive functions
Lec 6 (Jan 23): Derivative, gradient and Jacobian
Lec 7 (Jan 28): No lecture today
Lec 8 (Jan 30): More examples; PSD matrices, matrix-variate functions
Lec 9 (Feb 4): Log-determinant function and Hessian, multi-variate Taylor’s theorem
Lec 10 (Feb 6): Convex sets and functions
Lec 11 (Feb 11): Necessary and sufficient conditions
Lec 12 (Feb 13): Gradient descent and line search method
Lec 13 (Feb 18): Condition number and preconditioned gradient descent
Lec 14 (Feb 20): Newton’s method
Lec 15 (Feb 25): Quasi Newton method
Lec 16 (Feb 27): Rates of convergence for GD
Lec 17 (Mar 4): No Lecture today
Lec 18 (Mar 6): (No topic assigned)