Seminario del 2023
2023
23 gennaio
Gondzio Jacek
nel ciclo di seminari: "MODERN TECHNIQUES OF LARGE SCALE OPTIMIZATION FOR DATA SCIENCE"
Seminario di analisi numerica
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).