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Many problems in signal processing [e.g., filter bank design, independent component analysis (ICA), beamforming design, and neural network training] can be formulated as optimization over groups of transformations that depend continuously on real parameters (Lie groups). Such problems are usually tackled in two ways: using a constrained optimization procedure or using some parameterization to transform them into unconstrained problems.
Deep neural networks provide unprecedented performance gains in many real-world problems in signal and image processing. Despite these gains, the future development and practical deployment of deep networks are hindered by their black-box nature, i.e., a lack of interpretability and the need for very large training sets. 
Enabling autonomous driving (AD) can be considered one of the biggest challenges in today?s technology. AD is a complex task accomplished by several functionalities, with environment perception being one of its core functions. Environment perception is usually performed by combining the semantic information captured by several sensors, i.e., lidar or camera. The semantic information from the respective sensor can be extracted by using convolutional neural networks (CNNs) for dense prediction. In the past, CNNs constantly showed stateof-the-art performance on several vision-related tasks, such as semantic segmentation of traffic scenes using nothing but the red-green-blue (RGB) images provided by a camera. 
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, subdiffraction imaging, and astronomy. In each of these domains, the physics of the acquisition system dictates that only the magnitude (intensity) of certain linear projections of the signal or image can be measured. Without any assumptions on the unknown signal, accurate recovery necessarily requires an overcomplete set of measurements.

Zeroth-order (ZO) optimization is a subset of gradient-free optimization that emerges in many signal processing and machine learning (ML) applications. It is used for solving optimization problems similarly to gradient-based methods. However, it does not require the gradient, using only function evaluations. Specifically, ZO optimization iteratively performs three major steps: gradient estimation, descent direction computation, and the solution update. In this article, we provide a comprehensive review of ZO optimization, with an emphasis on showing the underlying intuition, optimization principles, and recent advances in convergence analysis.

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