Engineering Papers⌕ Search
Home/Archive/DOE OSTI

DOE OSTI · 1760566

Piecewise polyhedral formulations for a multilinear term

Sundar, Kaarthik·Nagarajan, Harsha·Linderoth, Jeff·Wang, Site·Bent, Russell
View original source ↗Read source document ↗Export metadata ↓

Abstract

Herein, we present a mixed-integer linear programming (MILP) formulation of a piecewise, polyhedral relaxation (PPR) of a multilinear term using its convex-hull representation. Based on the PPR’s solution, we also present a MILP formulation whose solutions are feasible for nonconvex, multilinear equations. We then present computational results showing the effectiveness of proposed formulations on standard benchmark nonlinear programs (NLPs) with multilinear terms and compare with a traditional formulation that is built using recursive bilinear groupings of multilinear terms.

Explore related subjects

42 ENGINEERINGConvex hullGlobal optimizationMultilinearPiecewise polyhedral relaxations

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sundar, Kaarthik, Nagarajan, Harsha, Linderoth, Jeff, Wang, Site, Bent, Russell. 2020-12-08. Piecewise polyhedral formulations for a multilinear term. https://doi.org/10.1016/j.orl.2020.12.002

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related reports

DOE OSTI2026

Large language models for transportation research: Methodologies, state of the art, and future opportunities

The rapid rise of large language models (LLMs) is transforming transportation research, with significant advancements emerging between 2023 and 2025, a period marked by the inception and swift growth of adopting and adapting LLMs for various transportation applications. Despite these significant advancements, however, a systematic review and synthesis of the existing literature remains lacking. This paper aims to fill this gap by providing a comprehensive review of the methodologies and applications of LLMs in transportation. We explore key applications, including autonomous driving, travel behavior prediction, and general transportation-related queries, alongside LLM methodologies such as zero- or few-shot learning, prompt engineering, and fine-tuning. From the review, critical research gaps are identified. From the methodological perspective, many of the research limitations can be addressed by integrating LLMs with existing tools and refining LLM architectures. From the application perspective, research opportunities for LLMs to address various transportation challenges are also explored. By synthesizing these findings, this review not only presents the state-of-the-art LLM adoption and adaptation in transportation, but also proposes future research directions as well as insights and recommendations for policymakers and practitioners, paving the way for greater LLM-driven research innovations in transportation in the future.

42 ENGINEERING↗