Geodesic
Critical Values of Multilinear Forms under Conic Constraints
Journal of convex analysis, Tome 31 (2024) no. 4, pp. 1227-1244
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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.
Classification : 15A18, 15A23, 90C26, 90C33
Mots-clés : Multilinear form, convex cone, variational inequality, complementarity problem, cone-constrained singular value 
@article{JCA_2024_31_4_JCA_2024_31_4_a10,
     author = {A. Seeger},
     title = {Critical {Values} of {Multilinear} {Forms} under {Conic} {Constraints}},
     journal = {Journal of convex analysis},
     pages = {1227--1244},
     year = {2024},
     volume = {31},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2024_31_4_JCA_2024_31_4_a10/}
}
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A. Seeger. Critical Values of Multilinear Forms under Conic Constraints. Journal of convex analysis, Tome 31 (2024) no. 4, pp. 1227-1244. http://geodesic.mathdoc.fr/item/JCA_2024_31_4_JCA_2024_31_4_a10/