Abstract

Let Φ:Πi=1rEi→R\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 EiE_i is equipped with its own closed convex cone KiK_i. We analyze the concept of critical point and critical value of Φ\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.

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Keywords

  • Multilinear form
  • convex cone
  • variational inequality
  • complementarity problem
  • cone-constrained singular value

Mathematics Subject Classification

15A18, 15A23, 90C26, 90C33

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Suggested citation

A. Seeger. “Critical Values of Multilinear Forms under Conic Constraints.” Journal of Convex Analysis 31 (2024), No. 4, 1227–1244. https://doi.org/10.68381/jca31061

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.