L1-Lp Minimization via a Distributed Smoothing Neurodynamic Approach for Robust Multi-View Three-Dimensional Space Localization

Qu, Youran; Yang, Jiao; Liu, Hong; Zhao, You; Wei, Xuekai

doi:10.3390/app16010403

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Open AccessArticle

L₁-L_p Minimization via a Distributed Smoothing Neurodynamic Approach for Robust Multi-View Three-Dimensional Space Localization

by

Youran Qu

¹,

Jiao Yang

²,

Hong Liu

¹,

You Zhao

^1,*

and

Xuekai Wei

³

¹

Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronics and Information Engineering, Southwest University, Chongqing 400715, China

²

Chongqing General Station of Exit and Entry Frontier Inspection, Chongqing 401147, China

³

School of Computer Science, Chongqing University, Chongqing 400044, China

^*

Author to whom correspondence should be addressed.

Appl. Sci. 2026, 16(1), 403; https://doi.org/10.3390/app16010403 (registering DOI)

Submission received: 20 November 2025 / Revised: 21 December 2025 / Accepted: 26 December 2025 / Published: 30 December 2025

(This article belongs to the Section Computing and Artificial Intelligence)

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Abstract

This paper presents a distributed smoothing neurodynamic approach for solving the

L_{1}

-

L_{p}

minimization problem, with application to robust and collaborative multi-view three-dimensional (3D) space localization. To handle the non-Lipschitz continuity gradients, a smooth approximation technique is introduced, yielding a distributed neurodynamic model that integrates classical smoothing neural networks with multi-agents consensus theory. Theoretical analysis guarantees the global convergence of each agent’s state to the optimal solution. The stability and convergence of the proposed approaches are rigorously proved using Lyapunov theory. Numerical experiments on multi-view 3D space localization in the presence of measurement noise demonstrate the method’s effectiveness and practical value for distributed visual computing.

Keywords: distributed L1-Lp minimization problem; neurodynamic approach; global convergence; multi-view 3D space localization

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MDPI and ACS Style

Qu, Y.; Yang, J.; Liu, H.; Zhao, Y.; Wei, X. L₁-L_p Minimization via a Distributed Smoothing Neurodynamic Approach for Robust Multi-View Three-Dimensional Space Localization. Appl. Sci. 2026, 16, 403. https://doi.org/10.3390/app16010403

AMA Style

Qu Y, Yang J, Liu H, Zhao Y, Wei X. L₁-L_p Minimization via a Distributed Smoothing Neurodynamic Approach for Robust Multi-View Three-Dimensional Space Localization. Applied Sciences. 2026; 16(1):403. https://doi.org/10.3390/app16010403

Chicago/Turabian Style

Qu, Youran, Jiao Yang, Hong Liu, You Zhao, and Xuekai Wei. 2026. "L₁-L_p Minimization via a Distributed Smoothing Neurodynamic Approach for Robust Multi-View Three-Dimensional Space Localization" Applied Sciences 16, no. 1: 403. https://doi.org/10.3390/app16010403

APA Style

Qu, Y., Yang, J., Liu, H., Zhao, Y., & Wei, X. (2026). L₁-L_p Minimization via a Distributed Smoothing Neurodynamic Approach for Robust Multi-View Three-Dimensional Space Localization. Applied Sciences, 16(1), 403. https://doi.org/10.3390/app16010403

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L₁-L_p Minimization via a Distributed Smoothing Neurodynamic Approach for Robust Multi-View Three-Dimensional Space Localization

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