Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)

Adeel Akhtar; Ricardo G. Sanfelice

doi:10.23919/ACC55779.2023.10155919

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 proceeding › Conference contribution › peer-review

Abstract

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 language	English (US)
Title of host publication	2023 American Control Conference, ACC 2023
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3554-3559
Number of pages	6
ISBN (Electronic)	9798350328066
DOIs	https://doi.org/10.23919/ACC55779.2023.10155919
State	Published - 2023
Event	2023 American Control Conference, ACC 2023 - San Diego, United States Duration: May 31 2023 → Jun 2 2023

Publication series

Name	Proceedings of the American Control Conference
Volume	2023-May
ISSN (Print)	0743-1619

Conference

Conference	2023 American Control Conference, ACC 2023
Country/Territory	United States
City	San Diego
Period	05/31/23 → 06/2/23

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

Access to Document

10.23919/ACC55779.2023.10155919

Cite this

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title = "Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)",

abstract = "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.",

author = "Adeel Akhtar and Sanfelice, {Ricardo G.}",

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: {\textcopyright} 2023 American Automatic Control Council.; 2023 American Control Conference, ACC 2023 ; Conference date: 31-05-2023 Through 02-06-2023",

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doi = "10.23919/ACC55779.2023.10155919",

language = "English (US)",

series = "Proceedings of the American Control Conference",

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Akhtar, A & Sanfelice, RG 2023, Global Accelerated Nonconvex Geometric Optimization Methods on SO(3). in 2023 American Control Conference, ACC 2023. Proceedings of the American Control Conference, vol. 2023-May, Institute of Electrical and Electronics Engineers Inc., pp. 3554-3559, 2023 American Control Conference, ACC 2023, San Diego, United States, 05/31/23. https://doi.org/10.23919/ACC55779.2023.10155919

Global Accelerated Nonconvex Geometric Optimization Methods on SO(3). / Akhtar, Adeel; Sanfelice, Ricardo G.
2023 American Control Conference, ACC 2023. Institute of Electrical and Electronics Engineers Inc., 2023. p. 3554-3559 (Proceedings of the American Control Conference; Vol. 2023-May).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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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.

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Global Accelerated Nonconvex Geometric Optimization Methods on SO(3)

Abstract

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