Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:46:00.228083Z
Paper Citation Record · LEDGER
As of 11 August 2026, this Paper Citation Record lists 79 of 79 outbound references and 1 inbound Pith citation observation for arXiv:2506.23758.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-06T21:46:00.228083Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-01T05:13:39.448136Z
A source-named dated measurement, never combined with another source.
Source: cited_works
79 of 79 outbound references displayed
External citation measurements
No source-named external measurement is stored.
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 1
Source-reported events for the cited work
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 2
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Bolte, A
Reference 3
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Observation 6ad6b61b-c8b5-4507-8160-688fee4b7fc5 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 4
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Randomized Derivative-Free Optimization of Noisy Convex Functions
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Choromanski, M
Reference 9
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 10
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Defazio, F
Reference 11
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Demetrio, B
Reference 12
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Reference 13
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Reference 14
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Flaxman, A
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 17
Source-reported events for the cited work
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Gasnikov, A
Reference 18
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Gautam, Y
Reference 19
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Ghadimi and G
Reference 20
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Observation f5f0917e-b6b0-4624-afd4-bfb66c1c434d · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Ghadimi, G
Reference 21
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Observation 7687bb2b-e260-4a97-8e95-ff97c744877d · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 22
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Observation 75baba36-40a7-4f44-8512-096c9866920f · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 23
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Huang, B
Reference 24
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Observation 0c3e54f1-0059-43ad-b3cd-57782fd7f033 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Huang, L
Reference 25
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Observation a42e2371-3986-4f6b-8ec1-deae3d5467fe · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 26
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Observation a142c905-c066-4bfc-a8cc-e4223eb8151b · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Ilyas, L
Reference 27
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Observation f4413090-3955-467b-a057-558b480c5ebc · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 28
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 29
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Observation 8620c38c-8ca6-4a4b-975d-c94e6cfe778d · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Johnson and T
Reference 30
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Observation 21f9a624-8e54-4df4-9d98-9c510f8db56c · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Kazemi and L
Reference 31
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Observation 9193979c-5a0f-4cd6-8afa-d64bec1074ee · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Stochastic Subspace Descent
Reference 32
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Observation f48ee480-cc11-4832-8491-a0e10a54c3a5 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Kozak, S
Reference 33
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Observation 2655878d-9564-4e19-a0d0-ad8f0120afba · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Kozak, C
Reference 34
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Lankham, B
Reference 35
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Observation 064fbd9e-65cc-4cd3-bb45-e9487aa19675 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 36
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Observation 9bae9d8f-55b7-495c-a3dc-1ff3e690c185 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Li and J
Reference 37
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Observation e509f224-5c12-4e5f-b245-ef320644f8bc · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 38
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Stochastic Zeroth-order Optimization via Variance Reduction method
Reference 39
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 40
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Reference 41
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Reference 42
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Observation cc4263c1-5de0-419a-8abf-cff5b83fc023 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 43
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Mezzadri
Reference 44
Source-reported events for the cited work
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Reference 45
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Observation a4d4ea2c-7505-4f57-b877-c3ce3459c21f · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 46
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Nesterov and V
Reference 47
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Observation 73314e59-f418-42a3-b929-3092db149ea6 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Paszke, S
Reference 48
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Observation e9b965d8-4d65-4c04-b54e-496589e445db · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 49
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Pougkakiotis and D
Reference 50
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Raffel, N
Reference 51
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Rando, L
Reference 52
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Rando, L
Reference 53
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Rando, C
Reference 54
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Rando, C
Reference 55
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Reference 56
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Reference 57
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Reference 58
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Reference 59
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 60
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Observation d5f45b7f-6f4e-4cc9-bdb6-01b70a1bcbde · outbound
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Reference 61
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Reference 62
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 63
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Wang and Y
Reference 64
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Observation 5130e947-7c23-49e2-a312-b8ee4d23bf5f · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Zhang, P
Reference 65
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Zhu and M
Reference 66
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A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm fi(x + βv) − fi(x) − ⟨∇fi(x), βv⟩ !2# + 3 d2 ℓβ2 EiEv
Reference 67
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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 748fc58b-c79f-44d7-8fac-48b8d05ecddb · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Noticing that F (xT +1 0 ) ≥ min F and dividing by ∆γm(T + 1), we conclude the proof: 1 (T + 1)m TX τ =0 m−1X k=0 E ∥Gγ(xτ k)∥2 ≤ E F (x0
Reference 68
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Observation b0ca4545-21ad-4edb-a95b-2821252672af · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Proof of Corollary 1 From Theorem 1, choosing the stepsize γ <min( 1 4L , √ ℓb 10Lm √ d ), we have 1 (T + 1)m TX τ =0 m−1X k=0 E ∥Gγ(xτ k)∥2 ≤ 10L √ d√ ℓb F (x0
Reference 69
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation dfc523b8-cef3-4e15-a38a-9689cce974ce · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Note that, due to the choice of the stepsize, ∆ ≥ 1
Reference 70
Source-reported events for the cited work
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Observation 1d92cc15-f20a-4587-a6bb-f29606e8862d · outbound
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Reference 71
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Observation 2ae53df3-d2eb-4e25-90a7-be0301f5cb3f · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm (24) Points (i) and (ii) can be proved by replacing the corresponding value of βτ in eq
Reference 72
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No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 7d8c6f62-051e-42cd-bb96-01e7e264f7ab · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm 28 Instead, with the choice βτ = β d (ii) we get 1 (T + 1)m TX τ =0 m−1X k=0 E ∥Gγ(xτ k)∥2 ≤ 40L √ d√ ℓb F (x0
Reference 73
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Observation 723c2c42-30e5-4a54-9b4c-ed3f2dd1bcd8 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm We prove point (iii) in a constructive way
Reference 74
Source-reported events for the cited work
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Observation d02d40fd-dd71-4faa-9bc1-4adf6302f4ba · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm If we impose, 40L √ d√ ℓb F (x0
Reference 75
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Observation aa1ba460-e1ad-40dd-af82-6cc18dcb4974 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 76
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Observation 7cbe79c0-2807-4f34-a2d6-e3ffc438edb2 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Unresolved cited work
Reference 77
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Observation edf1d23e-93d6-4d2e-a0a7-66fb0f06153b · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm m−1X k=0 C(γ) 2k + 2 1 αk+1 ∥xτ k+1 − xτ 0 ∥2 − m−1X k=0 1 αk+1 6d ℓb L2γ + C(γ) 2k + 1 ∥xτ k − xτ 0 ∥2 # = αmE [F (xτ 0 ) − min F ] + 1 − αm 1 − α 3d ℓb + 2 + 3d L2dγβ 2 τ − αmE
Reference 78
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Observation 04ee7740-b2a5-48d6-984f-4fbc7117d238 · outbound
A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm Proof of Corollary 2 By Theorem 2, we have E F xτ +1 0 − min F ≤ αm(τ +1) [F (x0) − min F ] + αm(τ +1) 1 − αm 1 − α γ 3L2d2 ℓ + L2d 2 τX i=0 β2 i αm(i+1) , where α = 1 − γµ 2
Reference 79
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Observation 9ca1c297-5b84-4cec-9b11-701bd9559af7 · inbound
Langevin for Nonconvex Optimization: Exact, Inexact and Zeroth-Order A Structured Proximal Stochastic Variance Reduced Zeroth-order Algorithm
Reference 65
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