Quadratic modules in real algebraic geometry are akin to polynomial ideals in algebraic geometry, and have been found useful in the theory of Positivstellensatz to study Hilbert's 17th problem. Algorithms are presented in this paper for testing ...

Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly infeasible linear matrix ...

A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine-linear combinations of variables is positive semidefinite. Motivated by the fact that diagonal LMIs define polyhedra, the solution set of an LMI is ...

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 ...