Journal of Convex Analysis 31 (2024), No. 4, 1227--1244
Copyright Heldermann Verlag 2024
Critical Values of Multilinear Forms under Conic Constraints
Alberto Seeger
Dept. of Mathematics, University of Avignon, Avignon, France
alberto.seeger@univ-avignon.fr
[Abstract-pdf]
Let $\Phi:\Pi_{i=1}^r E_i\to \mathbb{R}$ be a multilinear form on the Cartesian product of finitely many Euclidean vector spaces. We suppose that each factor $E_i$ is equipped with its own closed convex cone $K_i$. We analyze the concept of critical point and critical value of $\Phi$ 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.
Keywords: Multilinear form, convex cone, variational inequality, complementarity problem, cone-constrained singular value.
MSC: 15A18, 15A23, 90C26, 90C33.
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