{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/necessary-and-sufficient-conditions-for-31","title":"Necessary and sufficient conditions for multiple objective optimal regression designs","arxiv_id":"2303.04746","date":"2023-03-08","proceeding":null,"authors":["Lucy L. Gao","Jane J. Ye","Shangzhi Zeng","Julie Zhou"],"abstract":"We typically construct optimal designs based on a single objective function. To better capture the breadth of an experiment's goals, we could instead construct a multiple objective optimal design based on multiple objective functions. While algorithms have been developed to find multi-objective optimal designs (e.g. efficiency-constrained and maximin optimal designs), it is far less clear how to verify the optimality of a solution obtained from an algorithm. In this paper, we provide theoretical results characterizing optimality for efficiency-constrained and maximin optimal designs on a discrete design space. We demonstrate how to use our results in conjunction with linear programming algorithms to verify optimality.","url_abs":"https://arxiv.org/abs/2303.04746v1","url_pdf":"https://arxiv.org/pdf/2303.04746v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"necessary-and-sufficient-conditions-for-31","repo_url":"https://github.com/lucylgao/multi-objective-paper-code-2022","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}