Stefano Pironio

**STEFANO PIRONIO**Laboratoire d’Informatique Quantique

Université Libre de Bruxelles

Convex optimization problems are a class of optimization problems for which there exist efficient numerical solvers and which possess a rich theoretical structure. In particular, semidefinite programming, a subfield of a convex optimization, has found many applications in quantum information. In this series of lectures, I will introduce the basics of convex optimization and its duality theory and review, as an illustration, some applications in quantum information. The starting point will be linear programming, which is one of the simplest example of convex optimization. We will then move from linear programming to conic optimization, which encompasses semidefinite programming (and actually any convex optimization problem). We will then view some applications of semidefinite programming to quantum information (depending on the time available). Finally, I will explain how polynomial optimization problems can be solved through a hierarchy of semidefinite relaxations.

**Lecture 1 ’Linear Programming’ Tuesday, June 11, 2019, 10:15. ICFO’s Blue Lecture Room****Lecture 2 ’Conic Linear Programming’ Thursday, June 13, 2019, 10:15. ICFO’s Blue Lecture Room****Lecture 3 ’Some Applications to Quantum Information’ Tuesday, June 18, 2019, 10:15. ICFO’s Blue Lecture Room****Lecture 4 ’Semidefinite Programming Relaxation Hierarquies and Sum of Squares’ Wednesday, June 19, 2019, 14:15. ICFO’s Yellow Lecture Room**