Describing convex semialgebraic sets by linear matrix inequalities

摘要

A semialgebraic set is a set described by a boolean combination of real polynomial inequalities in several variables. A linear matrix inequality (LMI) is a condition expressing that a symmetric matrix whose entries are affine-linear combinations of variables is positive semidefinite. We call solution sets of LMIs spectrahedra and their linear images semidefinite representable.