Modern Techniques of Large Scale Optimization for Data Science part 1

Lectures 1 and 2 (2h) Interior Point Methods (IPMs) for LP - Motivation, logarithmic barrier function, central path, neighbourhoods, - path-following method, convergence proof, complexity of the algorithm, - practical implementation issues. Lectures 3 and 4 (2h) Interior Point Methods for QP, (convex) NLP, SOCP and SDP - Quadratic Programming (QP) problems, primal-dual pair of QPs, - Nonlinear (convex) inequality constraints, - Second-Order Cone Programming, - Semidefinite Programming, - Newton method, logarithmic barrier function, self-concordant barriers. Lectures 5 and 6 (2h) - Sparse Approximations with IPMs: modern applications of optimization which require a selection of a 'sparse' solution originating from computational statistics, signal or image processing, compressed sensing, machine learning, and discrete optimal transport, to mention just a few. - Alternating Direction Method of Multipliers (ADMM).