The Geometric Properties of a Class of Nonsymmetric Cones

Shiyun Wang ()
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Shiyun Wang: Shenyang Institute of Aeronautical Engineering

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 3, 989-1002

Abstract: Abstract Geometric methods are important for researching the differential properties of metric projectors, sensitivity analysis, and the augmented Lagrangian algorithm. Sun [3] researched the relationship among the strong second-order sufficient condition, constraint nondegeneracy, B-subdifferential nonsingularity of the KKT system, and the strong regularity of KKT points in investigating nonlinear semidefinite programming problems. Geometric properties of cones are necessary in studying second-order sufficient condition and constraint nondegeneracy. In this paper, we study the geometric properties of a class of nonsymmetric cones, which is widely applied in optimization problems subjected to the epigraph of vector k-norm functions and low-rank-matrix approximations. We compute the polar, the tangent cone, the linear space of the tangent cone, the critical cone, and the affine hull of this critical cone. This paper will support future research into the sensitivity and algorithms of related optimization problems.

Keywords: Critical cone; geometric properties; nonsymmetric cone; tangent cone; 65K10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0445-1

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