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)|
|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.|
|Number of pages||5|
|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
|Name||ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings|
|Conference||44th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2019|
|Period||5/12/19 → 5/17/19|
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