EURO 2024 Copenhagen
Abstract Submission

EURO-Online login

2549. Term-sparse polynomial optimization for the design of frame structures

Invited abstract in session WD-38: Advances in polynomial optimization and its applications, stream Conic Optimization: Theory, Algorithms, and Applications.

Wednesday, 14:30-16:00
Room: 34 (building: 306)

Authors (first author is the speaker)

1. MAROUAN HANDA
MTR, Institute of Information Theory and Automation of the CAS

Abstract

This work investigates 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. Recently, these problems where tackled using the moment-sum-of-squares (mSOS) hierarchy. However, only smaller instances can be solved 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). 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 larger instances and accelerate the solution of the problems significantly.

Keywords

Status: accepted

Back to the list of papers