# Conic Programming: Theory and applications

** Prof. Benedetto Manca**Università degli Studi di Cagliari

**Abstract**

The course covers the theory of conic programming, starting from the simplest case of linear programming and introducing conic quadratic and semi-definite programming. The first part of the course will introduce the theoretical backgrounds needed to define the concept of conic programming. In the second part the case of conic quadratic and semi-definite programming will be addressed together with some applications.

**Outline
**

- From Linear to Conic Programming
- Conic Quadratic Programming
- The quadratic formulation of the Distance Geometry Problem
- Semi-definite Programming
- The semi-definite relaxation of the Distance Geometry Problem
- Diagonally dominant matrices and positive semi-definite matrices
- The ellipsoidal separation problem

**Schedule**

The course consists in 10 hours, two lectures per week. Details will be specified on the occasion of the first lecture, which will be given on October 3, 2024 at 2:30 p.m. in room B of the Department of Mathematics and Computer Science.

**Exam**

The final exam consists in a presentation on a specific application of conic programming (conic quadratic or semi-definite).

**References**

- Ben-Tal, Aharon, and Arkadi Nemirovski. Lectures on modern convex optimization: analysis, algorithms, and engineering applications. Society for industrial and applied mathematics, 2001.
- Liberti, Leo. “Distance geometry and data science.” Top 28.2 (2020): 271-339
- Astorino, Annabella, et al. “Ellipsoidal classification via semidefinite programming.” Operations Research Letters 51.2 (2023): 197-203.