TY - GEN
T1 - Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)
AU - Akhtar, Adeel
AU - Sanfelice, Ricardo G.
N1 - 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.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85167807432&partnerID=8YFLogxK
U2 - 10.23919/ACC55779.2023.10155919
DO - 10.23919/ACC55779.2023.10155919
M3 - Conference contribution
AN - SCOPUS:85167807432
T3 - Proceedings of the American Control Conference
SP - 3554
EP - 3559
BT - 2023 American Control Conference, ACC 2023
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2023 American Control Conference, ACC 2023
Y2 - 31 May 2023 through 2 June 2023
ER -