{"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/second-order-optimality-conditions-for","title":"Second Order Optimality Conditions for Optimal Control Problems of Stochastic Evolution Equations","arxiv_id":"1811.07337","date":"2018-11-18","proceeding":null,"authors":["Qi Lu","Haisen Zhang","Xu Zhang"],"abstract":"In this paper, we establish some second order necessary/sufficient optimality conditions for optimal control problems of stochastic evolution equations in infinite dimensions. The control acts on both the drift and diffusion terms and the control region is convex. The concepts of relaxed and $V$-transposition solutions (introduced in our previous works) to operator-valued backward stochastic evolution equations are employed to derive these optimality conditions. The correction part of the second order adjoint equation, which does not appear in the (first order) Pontryagin-type stochastic maximum principle, plays a fundamental role in our second order optimality conditions.","url_abs":"https://arxiv.org/abs/1811.07337v1","url_pdf":"https://arxiv.org/pdf/1811.07337v1.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":"second-order-optimality-conditions-for","repo_url":"https://github.com/LvQiSCU/LvQiSCU.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}