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首页> 外文期刊>Signal Processing, IET >Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation
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Instantaneous magnitudes and instantaneous frequencies of signals with their positivity constraints via non-smooth non-convex functional constrained optimisation

机译：通过非平滑，非凸函数约束最优化，具有正约束的信号的瞬时幅度和瞬时频率

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摘要

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.
机译：本研究提出了一种迭代方法，通过一系列N个独立的一维优化问题来近似加权Lp范数和L2范数目标函数的N维优化问题。这种迭代方法的灵感来自于现有的加权L1范数和L2范数可分离替代函数（SSF）迭代收缩算法。但是，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，它们可能具有多个局部最优解。通常，很难找到其全局最佳解决方案。为了解决这个难题，本研究建议将每个近似问题的可行集划分为各个区域，以使每个区域中目标函数凸性的符号保持不变。在这种情况下，每个区域最多只能有一个固定点。通过在每个区域中找到固定点，可以找到每个近似优化问题的全局最优解。此外，该研究还表明，近似问题的全局最优解的序列收敛于原始优化问题的全局最优解。

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