Jan Quan, Panagiotis Patrinos · 2026 · arXiv (Cornell University)
DOI: 10.48550/arxiv.2610.28414 · cited by 0 works (OpenAlex) · open-access PDF
हम दो बंद, घूर्णन सेट प्रदान करते हैं, जिनके पास एक गैर-आउट सर्किट और एक प्रारंभिक बिंदु है जिसके लिए डगलस-रेचफोर्ड एल्गोरिथ्म कमजोर लेकिन मजबूत नहीं होता है। यह एक खुले सवाल को हल करता है जैसा कि Aragón Artacho, Borwein और Tam (2014, नोट 2.2) द्वारा पहले उल्लेख किया गया था।
Machine translation (Meta M2M100); the English original follows.
We provide two closed, convex sets with nonempty intersection and an initial point for which the Douglas-Rachford algorithm converges weakly but not strongly. This resolves an open question as noted earlier by Aragón Artacho, Borwein and Tam (2014, Remark 2.2). Our construction is a simple lift of a recent construction by Bauschke and Tung concerning firmly nonexpansive operators.
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Topics: Mathematics, Intersection (aeronautics), Regular polygon, Lift (data mining), Simple (philosophy), Point (geometry)
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