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The Geometric Properties of a Class of Nonsymmetric Cones

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  • Shiyun Wang

    (Shenyang Institute of Aeronautical Engineering)

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.

Suggested Citation

  • Shiyun Wang, 2020. "The Geometric Properties of a Class of Nonsymmetric Cones," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(3), pages 989-1002, September.
    • Handle: RePEc:spr:indpam:v:51:y:2020:i:3:d:10.1007_s13226-020-0445-1
    DOI: 10.1007/s13226-020-0445-1
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    References listed on IDEAS

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    1. N. Maculan & C.P. Santiago & E.M. Macambira & M.H.C. Jardim, 2003. "An O(n) Algorithm for Projecting a Vector on the Intersection of a Hyperplane and a Box in Rn," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 553-574, June.
    2. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
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