Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation
Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation
复制标题
信号的瞬时幅度和频率及其通过非光滑非平滑的正约束
DOI：
10.1049/iet-spr.2014.0234
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发表时间：
2016
影响因子：
1.7
通讯作者：
Ling BWK
中科院分区：
文献类型：
--
作者：
Yang Zhijing;Kuang Wei-Chao;Ling Bingo Wing-Kuen;Dai Qingyun;Ling BWK
本研究提出了一种迭代方法，通过N个独立的一维优化问题的序列来近似具有加权Lp范数和L2范数目标函数的N维优化问题。该迭代方法的灵感来自于现有的加权L1范数和L2范数可分离代理泛函（SSF）迭代收缩算法。然而，由于这些独立的一维优化问题由加权Lp范数和L2范数目标函数组成，因此这些优化问题是非凸的，并且它们可能有多个局部最优解。一般来说，很难找到它们的全局最优解。为了解决这个困难，本研究提出了分区的可行集的每个近似问题到各个区域，使在每个区域的目标函数的凸性的符号保持不变。在这种情况下，在每个区域中不存在多于一个静止点。通过在每个区域中找到稳定点，可以找到每个近似优化问题的全局最优解，并且证明了近似问题的全局最优解序列收敛到原优化问题的全局最优解.
This study proposes an iterative method to approximate an N‐dimensional optimisation problem with a weighted Lp norm and L2 norm objective function by a sequence of N independent one‐dimensional optimisation problems. This iterative method is inspired by the existing weighted L1 norm and L2 norm separable surrogate functional (SSF) iterative shrinkage algorithm. However, as these independent one‐dimensional optimisation problems consist of weighted Lp norm and L2 norm objective functions, these optimisation problems are non‐convex and they may have more than one locally optimal solutions. In general, it is very difficult to find their globally optimal solutions. To address this difficulty, this study proposes to partition the feasible set of each approximated problem into various regions such that the sign of the convexity of the objective function in each region remains unchanged. In this case, there is no more than one stationary point in each region. By finding the stationary point in each region, the globally optimal solution of each approximated optimisation problem can be found. Besides, this study also shows that the sequence of the globally optimal solutions of the approximated problems converge to the globally optimal solution of the original optimisation problem.