Term-sparse polynomial optimization for the design of frame structures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F25%3A00384191" target="_blank" >RIV/68407700:21110/25:00384191 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s11081-025-10000-5" target="_blank" >https://doi.org/10.1007/s11081-025-10000-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11081-025-10000-5" target="_blank" >10.1007/s11081-025-10000-5</a>

Result language

angličtina

Original language name

Term-sparse polynomial optimization for the design of frame structures

Original language description

This work investigates an efficient solution to two fundamental problems in topology optimization of frame structures. The first one involves minimizing structural compliance under linear-elastic equilibrium and weight constraint, while the second one minimizes the weight under compliance constraints. These problems are non-convex and generally challenging to solve globally, with the non-convexity concentrated in a polynomial matrix inequality. In Tyburec et al. (2021, 2023), the authors tackled the problems using the moment-sum-of-squares hierarchy (mSOS), but were only able to solve smaller instances globally. Here, we aim to improve the scalability of solution to these problems by using the mSOS hierarchy supplemented with the Term Sparsity Pattern technique (TSP), which was introduced by Magron and Wang (2023). Due to the unique polynomial structure of our problems in which the objective and constraint functions are separable polynomials, we further improve scalability by adopting a reduced monomial basis containing non-mixed terms only. From extensive numerical testing, we conclude that these techniques allow for a global solution to two times larger instances when compared to (Tyburec et al. 2021, 2023), and accelerate the solution of the problems from Tyburec et al. (2021, 2023) significantly.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GA22-15524S" target="_blank" >GA22-15524S: Polynomial optimization in the design of globally optimal frame structures under dynamic loads</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Optimization and Engineering

ISSN

1389-4420

e-ISSN

1573-2924

Volume of the periodical

26

Issue of the periodical within the volume

4

Country of publishing house

CH - SWITZERLAND

Number of pages

44

Pages from-to

2867-2910

UT code for WoS article

001514307200001

EID of the result in the Scopus database

2-s2.0-105008928967