Convex Predictor–Nonconvex Corrector Optimization Strategy with Application to Signal Decomposition

Laura Girometti (), Martin Huska (), Alessandro Lanza () and Serena Morigi ()
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Laura Girometti: University of Bologna
Martin Huska: University of Bologna
Alessandro Lanza: University of Bologna
Serena Morigi: University of Bologna

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 3, No 13, 1286-1325

Abstract: 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.

Keywords: Nonconvex optimization; Signal decomposition; Predictor–corrector; Cross-correlation; Multi-parameter selection; 65K10; 68U99 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02479-2

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