Critical Values of Multilinear Forms under Conic Constraints

Let

be a multilinear form on the Cartesian product of finitely many Euclidean vector spaces. We suppose that each factor

E_i E i

is equipped with its own closed convex cone

K_i K i

. We analyze the concept of critical point and critical value of

\Phi Φ

when each argument of this function is restricted to a normalization constraint and a conic constraint. Our study encompasses the theory of cone-constrained singular values of bilinear and trilinear forms.