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The linear coupling method was introduced recently by Allen-Zhu and Orecchia for solving convex optimization problems with first order methods, and it provides a conceptually simple way to integrate a gradient descent step and mirror descent step in each iteration.
Fast approximation algorithms for fractional packing and covering problems
Serge A. Plotkin, David B. Shmoys, and Éva Tardos · 1991
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A parallel approximation algorithm for positive linear programming
Michael Luby and Noam Nisan · 1993
Earlier work this paper cites.
Sequential and parallel algorithms for mixed packing and covering
Neal E. Young · 2001
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A fast approximation scheme for fractional covering problems with variable upper bounds
Lisa Fleischer · 2004
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Prox-method with rate of convergence O ( 1 / t ) O(1/t) for variational inequalities with Lipschitz continuous monotone operators and smooth convex-concave saddle point problems
Arkadi Nemirovski · 2004
Earlier work this paper cites.
Smooth minimization of non-smooth functions
Yurii Nesterov · 2005
Cited alongside, same era.
The multiplicative weights update method: a meta-algorithm and applications
Sanjeev Arora, Elad Hazan, and Satyen Kale · 2012
Cited alongside, same era.
Efficiency of coordinate descent methods on huge-scale optimization problems
Yurii Nesterov · 2012
Cited alongside, same era.
A nearly linear-time PTAS for explicit fractional packing and covering linear programs
Christos Koufogiannakis and Neal E. Young · 2014
Cited alongside, same era.
Efficient first-order methods for linear programming and semidefinite programming
James Renegar
Cited in the paper.
Neal E. Young · 2014
Later among the works it cites.
Linear coupling: An ultimate unification of gradient and mirror descent
Zeyuan Allen Zhu and Lorenzo Orecchia · 2014
Later among the works it cites.
Nearly-linear time positive LP solver with faster convergence rate
Zeyuan Allen-Zhu and Lorenzo Orecchia · 2015
Closest in time.
Using optimization to break the epsilon barrier: A faster and simpler width-independent algorithm for solving positive linear programs in parallel
Zeyuan Allen-Zhu and Lorenzo Orecchia · 2015
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