On Degenerate Doubly Nonnegative Projection Problems | PERPUSTAKAAN UNIVERSITAS KATOLIK PARAHYANGAN

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On Degenerate Doubly Nonnegative Projection Problems

Cui, Ying - Nama Orang; Sun, Defeng - Nama Orang; Toh, Kim-Chuan - Nama Orang; Liang, Ling - Nama Orang;

The doubly nonnegative (DNN) cone, being the set of all positive semidefinite matrices whose elements are nonnegative, is a popular approximation of the computationally intractable completely positive cone. The major difficulty for implementing a Newton-type method to compute the projection of a given large-scale matrix onto the DNN cone lies in the possible failure of the constraint nondegeneracy, a generalization of the linear independence constraint qualification for nonlinear programming. Such a failure results in the singularity of the Jacobian of the nonsmooth equation representing the Karush–Kuhn–Tucker optimality condition that prevents the semismooth Newton–conjugate gradient method from solving it with a desirable convergence rate. In this paper, we overcome the aforementioned difficulty by solving a sequence of better conditioned nonsmooth equations generated by the augmented Lagrangian method (ALM) instead of solving one aforementioned singular equation. By leveraging the metric subregularity of the normal cone associated with the positive semidefinite cone, we derive sufficient conditions to ensure the dual quadratic growth condition of the underlying problem, which further leads to the asymptotically superlinear convergence of the proposed ALM. Numerical results on difficult randomly generated instances and from the semidefinite programming library are presented to demonstrate the efficiency of the algorithm for computing the DNN projection to a very high accuracy.

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Barcode		Tipe Koleksi	Nomor Panggil	Lokasi	Status
art143759	null	Artikel		Gdg9-Lt3	Tersedia namun tidak untuk dipinjamkan - No Loan

Informasi Detail

Judul Seri: MATHEMATICS OF OPERATIONS RESEARCH; Vol.47 No.3 August 2022
No. Panggil: -
Penerbit: : .,
Deskripsi Fisik: p. 2219-2239
Bahasa: English
ISBN/ISSN: -
Klasifikasi: NONE
Tipe Isi: -
Tipe Media: -
Tipe Pembawa: -
Edisi: -
Subjek: SEMIDEFINITE PROGRAMMING
DEGENERACY
AUGMENTED LAGRANGIAN METHOD
DOUBLY NONNEGATIVE CONE
SEMISMOOTH NEWTON
METRIC SUBGERULARITY
Info Detail Spesifik: https://doi.org/10.1287/moor.2021.1205
Pernyataan Tanggungjawab: Ying Cui, Ling Liang, Defeng Sun, Kim-Chuan Toh

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