{"paper":{"title":"Blessing of High-Order Dimensionality: from Non-Convex to Convex Optimization for Sensor Network Localization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jiayu Zhang, Mingyu Lei, Yinyu Ye","submitted_at":"2023-08-04T12:08:23Z","abstract_excerpt":"This paper investigates the Sensor Network Localization (SNL) problem, which seeks to determine sensor locations based on known anchor locations and partially given anchors-sensors and sensors-sensors distances. Two primary methods for solving the SNL problem are analyzed: the low-dimensional method that directly minimizes a loss function, and the high-dimensional semi-definite relaxation (SDR) method that reformulates the SNL problem as an SDP (semi-definite programming) problem. The paper primarily focuses on the intrinsic non-convexity of the loss function of the low-dimensional method, whi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.02278","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2308.02278/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}