Matrix and tensor algebra. Notation. Differentiation.

Theory. Gradient. Convexity. Strong convexity. Lipschitz continuity. Limits on convergence rate. Constrained optimization. Dual function. Dual problem. Strong duality. Slater’s condition. Karush-Kuhn-Tucker condition.

Optimization methods. Gradient. Stochastic gradient. Conjugate gradient. Quasi-Newton. Subgradient. Proximal gradient. Accelerated gradient. Interior-point methods. ADMM. Adaptive gradient methods.