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PL^{。} is introduced in which paper?
The available sources trace the ordinary PL condition to Polyak’s early work, but the provided snippets do not identify any paper that first introduced the specific \(PL^\circ\) condition [1][2][3][5]. What the evidence supports The standard Polyak–Łojasiewicz condition is attributed to Polyak’s early work; one sour...
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openai.comCreate a landscape editorial hero image for this Studio Global article: PL^{。} is introduced in which paper?. Article summary: The available sources trace the ordinary PL condition to Polyak’s early work, but the provided snippets do not identify any paper that first introduced the specific \(PL^\circ\) condition [1][2][3][5].. Topic tags: general web, ai, code, growth, manufacturing. Reference image context from search candidates: Reference image 1: visual subject "# Polyak-Lojasiewicz Condition. * The Polyak–Łojasiewicz condition is a quantitative inequality that relates a function's suboptimality to the squared norm of its gradient, ensurin" source context "Polyak-Lojasiewicz Condition" Reference image 2: visual subject "# Polyak-Lojasiewicz Condition. * The Polyak–Łojasiewicz condition is a quantitative inequality that relates a function's suboptimality to the squared norm of its gra
Insufficient evidence. The available sources trace the ordinary PL condition to Polyak’s early work, but the provided snippets do not identify any paper that first introduced the specific (PL^\circ) condition .
What the evidence supports
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The standard Polyak–Łojasiewicz condition is attributed to Polyak’s early work; one source says Polyak proposed it in 1963 and that it is a special case of the Łojasiewicz inequality
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Another source states that the PL condition was introduced in Polyak’s early works
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A 2022 paper also refers to the Polyak–Łojasiewicz condition as “[Polyak, 1963]”
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What is not established
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What is the short answer to "PL^{。} is introduced in which paper?"?
The available sources trace the ordinary PL condition to Polyak’s early work, but the provided snippets do not identify any paper that first introduced the specific \(PL^\circ\) condition [1][2][3][5].
What are the key points to validate first?
The available sources trace the ordinary PL condition to Polyak’s early work, but the provided snippets do not identify any paper that first introduced the specific \(PL^\circ\) condition [1][2][3][5]. What the evidence supports The standard Polyak–Łojasiewicz condition is attributed to Polyak’s early work; one source says Polyak proposed it in 1963 and that it is a special case of the Łojasiewicz inequality [2].
What should I do next in practice?
Another source states that the PL condition was introduced in Polyak’s early works [1].
Sources
- arxiv.org[PDF] Lojasiewicz condition. - arXiv
- arxiv.orgarXiv:1608.04636v4 [cs.LG] 12 Sep 2020
- arxiv.orgOn the Lower Bound of Minimizing Polyak- Lojasiewicz ...
- arxiv.orgarXiv:2407.00812v2 [math.OC] 12 Feb 2025
- stat.cmu.edu[PDF] Lecture 13: February 28th 13.1 The Polyak-Lojasiewicz (PL) Condition
- ibm.comSELECT command (PL/I)
- ibm.comSELECT コマンド (PL/I)
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