{"paper":{"title":"Optimal Beamforming Structure and Efficient Optimization Algorithms for Generalized Multi-Group Multicast Beamforming Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Tianyu Fang, Yijie Mao","submitted_at":"2023-12-27T12:49:18Z","abstract_excerpt":"In this work, we focus on solving non-smooth non-convex maximization problems in multi-group multicast transmission. Leveraging Karush-Kuhn-Tucker (KKT) optimality conditions and successive incumbent transcending (SIT) duality, we thoroughly analyze the optimal beamforming structure for a set of optimization problems characterized by a general utility-based objective function. By exploiting the identified optimal structure, we further unveil inherent low-dimensional beamforming structures within the problems, which are asymptotically optimal in various regimes of transmit signal-to-noise ratio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.16559","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/2312.16559/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"}