Random Field Optimization

[2201.09951] Random Field Optimization Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2201.09951 (math) [Submitted on 24 Jan 2022] Title: Random Field Optimization Authors: Joshua L. Pulsipher , Benjamin R. Davidson , Victor M. Zavala View PDF HTML (experimental) Abstract: We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces (e.g., space and time) such as stochastic processes (e.g., time series, Gaussian processes, and Markov processes), random matrices, and random spatial fields. This paradigm involves sophisticated mathematical objects (e.g., stochastic differential equations and space-time kernel functions) and has been widely used in neuroscience, geoscience, physics, civil engineering, and computer graphics. Despite of this, however, random fields have seen limited use in optimization; specifically, existing optimization paradigms that involve uncertainty (e.g., stochastic programming and robust optimization) mostly focus on the use of finite random variables. This trend is rapidly changing with the advent of statistical optimization (e.g., Bayesian optimization) and multi-scale optimization (e.g., integration of molecular sciences and process engineering). Our work extends a recently-proposed abstraction for infinite-dimensional optimization problems by capturing more general uncertainty representations. Moreover, we discuss solution paradigms for this new class of problems based on finite transformations and sampling, and identify open questions and challenges. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2201.09951 [math.OC] (or arXiv:2201.09951v1 [math.OC] for this version) https://doi.org/10.48550/arXiv.2201.09951 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1016/j.compchemeng.2022.107854 Focus to learn more DOI(s) linking to related resources Submission history From: Joshua Pulsipher [ view email ] [v1] Mon, 24 Jan 2022 21:07:48 UTC (2,292 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2022-01 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

Related documents

• Random Field Optimization#682360
• Efficient Near Field Beam Tracking via Thompson Sampling#614995
• Efficient Near Field Beam Tracking via Thompson Sampling#614028
• Randomized Algorithms#3284
• AdaMeZO: Adam-style Zeroth-Order Optimizer for LLM Fine-tuning Without Maintaining the Moments#151739