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We study the problem of chasing convex bodies online: given a sequence of convex bodies $K_t\subseteq \mathbb{R}^d$ the algorithm must respond with points $x_t\in K_t$ in an online fashion (i.e., $x_t$ is chosen before $K_{t+1}$ is revealed).
An optimal on-line algorithm for metrical task system
Allan Borodin, Nathan Linial, and Michael E. Saks · 1992
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An optimal on-line algorithm for metrical task system
Allan Borodin, Nathan Linial, and Michael E. Saks · 1992
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On convex body chasing
Joel Friedman and Nathan Linial · 1993
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On the k-server conjecture
Elias Koutsoupias and Christos H Papadimitriou · 1995
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Centres of convex sets in
Krzysztof Przesławski · 1996
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Geometric nonlinear functional analysis. Vol. 1
Yoav Benyamini and Joram Lindenstrauss · 2000
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Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Ahron Ben-Tal and Arkadi Nemirovski · 2001
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Second-order cone programming
Farid Alizadeh and Donald Goldfarb · 2003
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Online chasing problems for regular polygons
Hiroshi Fujiwara, Kazuo Iwama, and Kouki Yonezawa · 2008
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Convex bodies: the Brunn-Minkowski theory
Rolf Schneider · 2014
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The generalized work function algorithm is competitive for the generalized 2-server problem
René Sitters · 2014
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Chasing convex bodies and functions
Antonios Antoniadis, Neal Barcelo, Michael Nugent, Kirk Pruhs, Kevin Schewior, and Michele Scquizzato · 2016
Cited alongside, same era.
Nested convex bodies are chaseable
Nikhil Bansal, Martin Böhm, Marek Eliáš, Grigorios Koumoutsos, and Seeun William Umboh · 2018
Cited alongside, same era.
Chasing nested convex bodies nearly optimally
Sébastien Bubeck, Bo’az Klartag, Yin Tat Lee, Yuanzhi Li, and Mark Sellke · 2018
Later among the works it cites.
Smoothed online convex optimization in high dimensions via online balanced descent
Niangjun Chen, Gautam Goel, and Adam Wierman · 2018
Later among the works it cites.
A nearly-linear bound for chasing nested convex bodies
C.J. Argue, Sébastien Bubeck, Michael B. Cohen, Anupam Gupta, and Yin Tat Lee · 2019
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Competitively chasing convex bodies
Sébastien Bubeck, Yin Tat Lee, Yuanzhi Li, and Mark Sellke · 2019
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Beyond online balanced descent: An optimal algorithm for smoothed online optimization
Gautam Goel, Yiheng Lin, Haoyuan Sun, and Adam Wierman · 2019
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Chasing convex bodies optimally
Mark Sellke · 2019
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