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Current discrete-time neurodynamics predominantly addresses unperturbed optimization scenarios, exhibiting inherent sensitivity to external noise, which limits the practical application of these methods. To address this issue, we propose a discrete-time noise-suppressed neurodynamics (DTNSN) model in this paper. First, the model integrates the static optimization stability of the gradient-based neurodynamics (GND) model with the time-varying tracking capability of the zeroing neurodynamics (ZND) model. Then, an integral feedback term is introduced to suppress external noise disturbances, thereby enhancing the robustness of the model. Additionally, to facilitate implementation on digital hardware, we employ an explicit linear three-step discretization method to obtain the proposed DTNSN model. Finally, the convergence performance, noise suppression capability, and practicality of the model are validated through theoretical analysis, numerical simulations, and acoustic source localization experiments. The model is applicable to the fields of intelligent control systems, acoustic signal processing, and industrial automation, providing new tools for real-time optimization in noisy environments.<\/jats:p>","DOI":"10.3390\/sym17060932","type":"journal-article","created":{"date-parts":[[2025,6,12]],"date-time":"2025-06-12T03:59:17Z","timestamp":1749700757000},"page":"932","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Discrete-Time Neurodynamics Scheme for Time-Varying Nonlinear Optimization with Equation Constraints and Application to Acoustic Source Localization"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0009-0007-2976-8389","authenticated-orcid":false,"given":"Yinqiao","family":"Cui","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6126-3486","authenticated-orcid":false,"given":"Zhiyuan","family":"Song","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7101-3333","authenticated-orcid":false,"given":"Keer","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8657-7023","authenticated-orcid":false,"given":"Jian","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-2816-8398","authenticated-orcid":false,"given":"Chuncheng","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9808-3419","authenticated-orcid":false,"given":"Daoheng","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Guangdong Ocean University, Zhanjiang 524088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,6,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kizielewicz, B., and Sa\u0142abun, W. 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