A variational approach to copositive matrices

Jean-Baptiste Hiriart-Urruty (1) , Alberto Seeger (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 AU - Avignon Université

This work surveys essential properties of the so-called copositive matrices, the study of which has been spread over more than fifty-five years. Special emphasis is given to varia-tional aspects related to the concept of copositivity. In addition, some new results on the geometry of the cone of copositive matrices are presented here for the first time.

Mots clés: copositive matrix; copositivity test; convex cone; Pareto eigenvalues; quadratic programming; copositive programming

Domaines: Mathématiques [math]

Jean-Baptiste Hiriart-Urruty, Alberto Seeger. A variational approach to copositive matrices. SIAM Review, 2010, 52 (4), pp.593-629. ⟨10.1137/090750391⟩. ⟨hal-00629655⟩