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The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously.
“Performance of optimal transmitter power control in cellular system,”
J. Zander, · 1992
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“Distributed cochannel interference control in cellular radio systems,”
J. Zander, · 1992
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“A simple distributed autonomous power control algorithm and its convergence,”
G.J. Foschini and Z. Miljanic, · 1993
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“Gradient-based learning applied to document recognition,”
Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, · 1998
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Nonlinear Programming, 2nd ed
D. Bertsekas, · 1999
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“Optimal and suboptimal transmit beamforming,”
M. Bengtsson and B. Ottersten, · 2001
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“The concave-convex procedure,”
A. L. Yuille and A. Rangarajan, · 2003
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“Linear precoding via conic optimization for fixed MIMO receivers,”
A. Wiesel, Y. C. Eldar, and S. Shamai(Shitz), · 2006
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“A generalized iterative water-filling algorithm for distributed power control in the presence of a jammer,”
R. H. Gohary, Y. Huang, Z.-Q. Luo, and J.-S. Pang, · 2009
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“Subgradient methods for saddle-point problems,”
A. Nedić and A. Ozdaglar, · 2009
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“Monotonic convergence of distributed interference pricing in wireless networks,”
C. Shi, R. A. Berry, and M. L. Honig, · 2009
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“Distributed sparse linear regression,”
G. Mateos, J. A. Bazerque, and G. B. Giannakis, · 2010
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Q. Shi, M. Razaviyayn, Z.-Q. Luo, and C. He, · 2011
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“Max-min fairness linear transceiver design for a multi-user MIMO interference channel,”
Y.-F Liu, Y.-H. Dai, and Z.-Q. Luo, · 2013
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“Linear transceiver design for a MIMO interfering broadcast channel achieving max-min fairness,”
M. Razaviyayn, M. Hong, and Z.-Q. Luo, · 2013
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“A unified convergence analysis of block successive minimization methods for nonsmooth optimization,”
M. Razaviyayn, M. Hong, and Z.-Q. Luo, · 2013
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“Comparison of distributed beamforming algorithms for MIMO interference networks,”
D. A. Schmidt, C. Shi, R. A. Berry, M. L. Honig, and W. Utschick, · 2013
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“Joint downlink base station association and power control for max-min fairness: Computation and complexity,”
R. Sun, M. Hong, and Z.-Q. Luo, · 2014
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“Optimal primal-dual methods for a class of saddle point problems,”
Y. Chen, G. Lan, and Y. Ouyang, · 2014
Cited alongside, same era.
“Successive convex approximation: Analysis and applications,”
M. Razaviyayn, · 2014
Cited alongside, same era.
“Decomposition by partial linearization: Parallel optimization of multi-agent systems,”
G. Scutari, F. Facchinei, P. Song, D. P. Palomar, and J.-S. Pang, · 2014
Cited alongside, same era.
“Flexible parallel algorithms for big data optimization,”
F. Facchinei, S. Sagratella, and G. Scutari, · 2014
Cited alongside, same era.
“Semi-asynchronous routing for large scale hierarchical networks,”
W. Liao, M. Hong, H. Farmanbar, and Z.-Q. Luo, · 2015
Cited alongside, same era.
“Decentralized learning for wireless communications and networking,”
G. B. Giannakis, Q. Ling, G. Mateos, I. D. Schizas, and H. Zhu, · 2015
“ASY-SONATA: Achieving geometric convergence for distributed asynchronous optimization,”
Y. Tian, Y. Sun, B. Du, and G. Scutari, · 2018
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“Convergence rate of distributed convex and nonconvex optimization methods with gradient tracking,”
A. Daneshmand, Y. Sun, and G. Scutari, · 2018
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“Robust optimization over multiple domains,”
Q. Qian, S. Zhu, J. Tang, R. Jin, B. Sun, and H. Li, · 2018
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“An inexact primal-dual smoothing framework for large-scale non-bilinear saddle point problems,”
K. T. L. Hien, R. Zhao, and W. B. Haskell, · 2018
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“The limit points of (optimistic) gradient descent in min-max optimization,”
C. Daskalakis and I. Panageas, · 2018
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Cited alongside, same era.
“Multicell coordinated beamforming with rate outage constraint—part ii: Efficient approximation algorithms,”
W. Li, T. Chang, and C. Chi, · 2015
Cited alongside, same era.
“Multicell coordinated beamforming with rate outage constraint—part i: Complexity analysis,”
W. Li, T.-H. Chang, and C. Chi, · 2015
Cited alongside, same era.
“Parallel selective algorithms for nonconvex big data optimization,”
F. Facchinei, G. Scutari, and S. Sagratella, · 2015
Cited alongside, same era.
“Next: In-network nonconvex optimization,”
P. Di Lorenzo and G. Scutari, · 2016
Cited alongside, same era.
“A unified algorithmic framework for block-structured optimization involving big data,”
M. Hong, M. Razaviyayn, Z.-Q. Luo, and J.-S. Pang, · 2016
Cited alongside, same era.
“Gradient descent only converges to minimizers,”
J. D. Lee, M. Simchowitz, M. I. Jordan, and B. Recht, · 2016
Cited alongside, same era.
“Mirror descent in saddle-point problems: Going the extra (gradient) mile,”
P. Mertikopoulos, H. Zenati, B. Lecouat, C.-S. Foo, V. Chandrasekhar, and G. Piliouras, · 2018
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“Non-convex min-max optimization: Provable algorithms and applications in machine learning,”
H. Rafique, M. Liu, Q. Lin, and T. Yang, · 2018
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“On the convergence and robustness of training GANs with regularized optimal transport,”
M. Sanjabi, B. Jimmy, M. Razaviyayn, and J. D. Lee, · 2018
Later among the works it cites.
“Solving non-convex non-concave min-max games under polyak-lojasiewicz condition,”
M. Sanjabi, M. Razaviyayn, and J. D. Lee, · 2018
Later among the works it cites.
“Understand the dynamics of GANs via primal-dual optimization,”
S. Lu, R. Singh, X. Chen, Y. Chen, and M. Hong, · 2018
Later among the works it cites.
“Block alternating optimization for non-convex min-max problems: algorithms and applications in signal processing and communications,”
S. Lu, I. Tsaknakis, and M. Hong, · 2019
Closest in time.
“GNSD: A gradient-tracking based nonconvex stochastic algorithm for decentralized optimization,”
S. Lu, X. Zhang, H. Sun, and M. Hong, · 2019
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“Spatial transmitter density allocation for frequency-selective wireless ad hoc networks,”
S. Lu and Z. Wang, · 2019
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“Training optimization and performance of single cell uplink system with massive-antennas base station,”
S. Lu and Z. Wang, · 2019
Closest in time.
“Solving a class of non-convex min-max games using iterative first order methods,”
M. Nouiehed, M. Sanjabi, T. Huang, J. D. Lee, and M. Razaviyayn, · 2019
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“On gradient descent ascent for nonconvex-concave minimax problems,” 2019
T. Lin, C. Jin, and M. I. Jordan, · 2019
Closest in time.
“Efficient algorithms for smooth minimax optimization,”
K. K. Thekumparampil, P. Jain, P. Netrapalli, and S. Oh, · 2019
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“Hybrid block successive approximation for one-sided non-convex min-max problems: Algorithms and applications, supplementary material,”
S. Lu, I. Tsaknakis, M. Hong, and Y. Chen, · 2020
Closest in time.