Abstract
The min-max problem, also known as the saddle point problem, can be used to formulate a wide range of applications in signal processing and wireless communications. However, existing optimization theory and methods, which mostly deal with problems with certain convex-concave structure, are not applicable for the aforementioned applications, which oftentimes involve non-convexity. In this work, we consider a general block-wise one-sided non-convex min-max problem, in which the minimization problem consists of multiple blocks and is non-convex, while the maximization problem is (strongly) concave. We propose two simple algorithms, which alternatingly perform one gradient descent-type step for each minimization block and one gradient ascent-type step for the maximization problem. For the first time, we show that such simple alternating min-max algorithms converge to first-order stationary solutions. We conduct numerical tests on a robust learning problem, and a wireless communication problem in the presence of jammers, to validate the efficiency of the proposed algorithms.
Original language | English (US) |
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Title of host publication | 2019 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Proceedings |
Publisher | Institute of Electrical and Electronics Engineers Inc. |
Pages | 4754-4758 |
Number of pages | 5 |
ISBN (Electronic) | 9781479981311 |
DOIs | |
State | Published - May 2019 |
Event | 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 - Brighton, United Kingdom Duration: May 12 2019 → May 17 2019 |
Publication series
Name | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |
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Volume | 2019-May |
ISSN (Print) | 1520-6149 |
Conference
Conference | 44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019 |
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Country/Territory | United Kingdom |
City | Brighton |
Period | 5/12/19 → 5/17/19 |
Bibliographical note
Publisher Copyright:© 2019 IEEE.