Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)

Adeel Akhtar*, Ricardo G. Sanfelice

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This paper proposes global accelerated nonconvex geometric (GANG) optimization algorithms for optimizing a class of nonconvex functions on the compact Lie group SO(3). Nonconvex optimization is a challenging problem because the objective function may have multiple critical points, including saddle points. We propose two accelerated geometric algorithms to escape maxima and saddle points using random perturbations. The first algorithm uses the value of the Hessian of the objective function and random perturbations to escape the undesired critical points. In contrast, the second algorithm uses only the gradient information and random perturbations to escape maxima and saddle points. The efficacy of these geometric algorithms is verified in simulations.

Original languageEnglish (US)
Title of host publication2023 American Control Conference, ACC 2023
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9798350328066
StatePublished - 2023
Event2023 American Control Conference, ACC 2023 - San Diego, United States
Duration: May 31 2023Jun 2 2023

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2023 American Control Conference, ACC 2023
Country/TerritoryUnited States
CitySan Diego

Bibliographical note

Funding Information:
This research has been partially supported by the National Science Foundation under Grant no. ECS-1710621, Grant no. CNS-2039054, and Grant no. CNS-2111688, by the Air Force Office of Scientific Research under Grant nos. FA9550-19-1-0169, FA9550-20-1-0238, and FA9550-23-1-0145, by the Air Force Research Laboratory under Grant nos. FA8651-22-1-0017 and FA8651-23-1-0004, and by the Army Research Office under Grant no. W911NF-20-1-0253.

Publisher Copyright:
© 2023 American Automatic Control Council.

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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