摘要翻译：
雷达接收滤波器和波形的联合设计是非凸的，但对于固定的接收滤波器，在优化波形的同时单独凸，反之亦然。这类问题是最优化中经常遇到的问题，也是双凸程序中经常遇到的问题。交替最小化(AM)可能是处理双凸性的最有效、最简单的算法。在本文中，我们通过优化文献中的旧的、成熟的问题来考虑这个问题的新观点。文中具体说明了雷达波形优化问题可分为约束最小二乘、半定规划(SDP)和二次约束二次规划(QCQP)。双凸约束在交替最小化中引入了对每次迭代变化的集合。我们证明了具有双凸约束的双凸问题交替极小化的收敛性，给出了它与具有约束笛卡尔积凸集但具有小直径凸壳的双凸问题的等价性。
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英文标题：
《Constrained Least Squares, SDP, and QCQP Perspectives on Joint Biconvex
  Radar Receiver and Waveform design》
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作者：
Pawan Setlur, Sean O'Rourke, Muralidhar Rangaswamy
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  Joint radar receive filter and waveform design is non-convex, but is individually convex for a fixed receiver filter while optimizing the waveform, and vice versa. Such classes of problems are fre- quently encountered in optimization, and are referred to biconvex programs. Alternating minimization (AM) is perhaps the most popu- lar, effective, and simplest algorithm that can deal with bi-convexity. In this paper we consider new perspectives on this problem via older, well established problems in the optimization literature. It is shown here specifically that the radar waveform optimization may be cast as constrained least squares, semi-definite programs (SDP), and quadratically constrained quadratic programs (QCQP). The bi-convex constraint introduces sets which vary for each iteration in the alternat- ing minimization. We prove convergence of alternating minimization for biconvex problems with biconvex constraints by showing the equivalence of this to a biconvex problem with constrained Cartesian product convex sets but for convex hulls of small diameter.
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PDF链接：
https://arxiv.org/pdf/1802.06513