Cyclic Projections in Hadamard Spaces

Alexander Lytchak; Anton Petrunin

doi:10.1007/s10957-022-02043-w

Cyclic Projections in Hadamard Spaces

Alexander Lytchak
, Anton Petrunin

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Bačák. Namely, we construct an example of convex subsets in a Hadamard space such that the corresponding cyclic product of projections is not asymptotically regular.

Original language	English (US)
Pages (from-to)	636-642
Number of pages	7
Journal	Journal of Optimization Theory and Applications
Volume	194
Issue number	2
DOIs	https://doi.org/10.1007/s10957-022-02043-w
State	Published - Aug 2022

All Science Journal Classification (ASJC) codes

Management Science and Operations Research
Control and Optimization
Applied Mathematics

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10.1007/s10957-022-02043-w

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title = "Cyclic Projections in Hadamard Spaces",

abstract = "We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Ba{\v c}{\'a}k. Namely, we construct an example of convex subsets in a Hadamard space such that the corresponding cyclic product of projections is not asymptotically regular.",

author = "Alexander Lytchak and Anton Petrunin",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",

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N2 - We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Bačák. Namely, we construct an example of convex subsets in a Hadamard space such that the corresponding cyclic product of projections is not asymptotically regular.

AB - We show that cyclic products of projections onto convex subsets of Hadamard spaces can behave in a more complicated way than in Hilbert spaces, resolving a problem formulated by Miroslav Bačák. Namely, we construct an example of convex subsets in a Hadamard space such that the corresponding cyclic product of projections is not asymptotically regular.

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UR - https://www.scopus.com/pages/publications/85132281196#tab=citedBy

U2 - 10.1007/s10957-022-02043-w

DO - 10.1007/s10957-022-02043-w

M3 - Article

AN - SCOPUS:85132281196

SN - 0022-3239

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SP - 636

EP - 642

JO - Journal of Optimization Theory and Applications

JF - Journal of Optimization Theory and Applications

IS - 2

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Cyclic Projections in Hadamard Spaces

Abstract

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