Introduction

Abstract

Semidefinite programming is a rich class of optimization problems with (generalized) convex constraints. Constraints in a semidefinite programming problem take the form of linear matrix inequalities. Such inequalities specify bounds on the eigenvalues of linear combinations of symmetric or Hermitian matrices. This way of modeling constraints is common practice in control theory, but it is still unusual in other branches of research. However, semidefinite programming has a great potential of application outside control theory, since many types of (generalized) convex functions can be modeled by linear matrix inequalities, even if the underlying problem has no obvious relation to matrix theory.