Convex Predictor–Nonconvex Corrector Optimization Strategy with Application to Signal Decomposition
提出一种预测-校正策略，先用凸优化得到全局候选解，再用非凸优化精调，高效求解非凸优化问题，并成功应用于一维信号分解为平滑、分段常数、振荡和噪声等语义成分。
Abstract Many tasks in real life scenarios can be naturally formulated as nonconvex optimization problems. Unfortunately, to date, the iterative numerical methods to find even only the local minima of these nonconvex cost functions are extremely slow and strongly affected by the initialization chosen. We devise a predictor–corrector strategy that efficiently computes locally optimal solutions to these problems. An initialization-free convex minimization allows to predict a global good preliminary candidate, which is then corrected by solving a parameter-free nonconvex minimization. A simple algorithm, such as alternating direction method of multipliers works surprisingly well in producing good solutions. This strategy is applied to the challenging problem of decomposing a 1D signal into semantically distinct components mathematically identified by smooth, piecewise-constant, oscillatory structured and unstructured (noise) parts.