mlsanityData to 14 Oct 2026

Formation Shape Control using the Gromov-Wasserstein Metric

arXiv 2503.21538 ↗First posted 27 Mar 2025math.OC cs.LG cs.MAcited by 2

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Abstract (arXiv)

This article introduces a formation shape control algorithm, in the optimal control framework, for steering an initial population of agents to a desired configuration via employing the Gromov-Wasserstein distance. The underlying dynamical system is assumed to be a constrained linear system and the objective function is a sum of quadratic control-dependent stage cost and a Gromov-Wasserstein terminal cost. The inclusion of the Gromov-Wasserstein cost transforms the resulting optimal control problem into a well-known NP-hard problem, making it both numerically demanding and difficult to solve with high accuracy. Towards that end, we employ a recent semi-definite relaxation-driven technique to tackle the Gromov-Wasserstein distance. A numerical example is provided to illustrate our results.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 11 of its 31 references that are in the map. First posted on arXiv 27 Mar 2025.

Builds on

11 of 31 references.

References · 11

  1. 2018Optimal Transport for structured data with application on graphscited by 172
  2. 2019Gromov-Wasserstein Learning for Graph Matching and Node Embeddingcited by 126
  3. 2018Gromov-Wasserstein Alignment of Word Embedding Spacescited by 122
  4. 2019Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matchingcited by 103
  5. 2020The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxationcited by 56
  6. 2022First-Order Methods for Nonsmooth Nonconvex Functional Constrained Optimization with or without Slater Pointscited by 17
  7. 2015Optimal transport over a linear dynamical systemcited by 14
  8. 2023Semidefinite Relaxations of the Gromov-Wasserstein Distancecited by 10
  9. 2023Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spacescited by 7
  10. 2024Minimum energy density steering of linear systems with Gromov-Wasserstein terminal costcited by 3
  11. 2023The Exact Projective Penalty Method for Constrained Optimizationcited by 1

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Cited by year

Citing papers per year: 2025: 2.

2 papers.

  1. 2025Data-Driven Density Steering via the Gromov-Wasserstein Optimal Transport Distancecited by 0
  2. 2025Fixed Horizon Linear Quadratic Covariance Steering in Continuous Time with Hilbert-Schmidt Terminal Costcited by 0