# Numerical Analysis and Scientific Computing Seminar

## Solving Conic Optimization Problems with MOSEK

**Speaker:**
Erling Andersen, MOSEK

**Location:**
Warren Weaver Hall 1302

**Date:**
Jan. 27, 2017, 10 a.m.

**Synopsis:**

A conic optimization problem minimizes a linear function over an affine set intersected by a convex cone. Even though the convex cone is restricted to be a so-called symmetric cone many convex optimization problems belong to this class of problems. Some examples that can be cast as a conic optimization problems are convex quadratic programs, sum of norms problems, linear least squares problems with linear constraints and eigenvalue optimization problems.

The presentation will begin with a brief introduction to conic optimization followed by an introduction to the software package MOSEK a state-of-the-art software packages for conic optimization problems. Some details about the algorithm and numerical linear algebra employed inside MOSEK will be discussed, as well as other issues such as infeasibility detection. Finally, benchmark results will be presented that illustrates large-scale sparse conic optimization problems can be solved efficiently. Moreover, we will show that MOSEK is currently the best optimizer for general semidefinite optimization problems.