Sion’s Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm | PERPUSTAKAAN UNIVERSITAS KATOLIK PARAHYANGAN

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Sion’s Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm

Zhang, Peiyuan - Nama Orang; Sra, Suvrit - Nama Orang; Zhang, Jingzhao - Nama Orang;

Deciding whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable. This paper takes a step towards understanding a broad class of nonconvex-nonconcave minimax problems that do remain tractable. Specifically, it studies minimax problems over geodesic metric spaces, which provide a vast generalization of the usual convex-concave saddle point problems. The first main result of the paper is a geodesic metric space version of Sion’s minimax theorem; we believe our proof is novel and broadly accessible as it relies on the finite intersection property alone. The second main result is a specialization to geodesically complete Riemannian manifolds: here, we devise and analyze the complexity of first-order methods for smooth minimax problems.

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Barcode		Tipe Koleksi	Nomor Panggil	Lokasi	Status
art148064	null	Artikel		Gdg9-Lt3	Tersedia namun tidak untuk dipinjamkan - No Loan

Informasi Detail

Judul Seri: SIAM JOURNAL ON OPTIMIZATION; Vol.33, No.4 October 2023-December 2023
No. Panggil: -
Penerbit: : .,
Deskripsi Fisik: p. 2885-2908
Bahasa: English
ISBN/ISSN: -
Klasifikasi: NONE
Tipe Isi: -
Tipe Media: -
Tipe Pembawa: -
Edisi: -
Subjek: GAME THEORY
EXTRAGRADIENT
RIEMANNIAN OPTIMIZATION
MINIMAX
GEODESIC CONVEXITY
Info Detail Spesifik: https://doi.org/10.1137/22M1505475
Pernyataan Tanggungjawab: Peiyuan Zhang, Jingzhao Zhang, Suvrit Sra

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