An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications

Hans Steven Aguilar Mendoza; Erik Alex Papa Quiroz; Miguel Angel Cano Lengua

doi:10.1109/EIRCON52903.2021.9613264

An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications

Hans Steven Aguilar Mendoza, Erik Alex Papa Quiroz, Miguel Angel Cano Lengua

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

1 Scopus citations

Abstract

This paper aims to identify the current state of the art of the latest research related to Conjugate Gradient (CG) methods for unconstrained optimization through a systematic literature review according to the methodology proposed by Kitchenham and Charter, to answer the following research questions: Q1: In what research areas are the conjugate gradient method used? Q2: Can Dai-Yuan conjugate gradient algorithm be effectively applied in portfolio selection? Q3: Have conjugate gradient methods been used to develop large-scale numerical results? Q4: What conjugate gradient methods have been used to minimize quasiconvex or nonconvex functions? We obtain useful results to extend the applications of the CG methods, develop efficient algorithms, and continue studying theoretical convergence results.

Original language	English
Title of host publication	Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781665444453
DOIs	https://doi.org/10.1109/EIRCON52903.2021.9613264
State	Published - 2021
Event	2nd IEEE Engineering International Research Conference, EIRCON 2021 - Virtual, Lima, Peru Duration: 27 Oct 2021 → 29 Oct 2021

Publication series

Name	Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021

Conference

Conference	2nd IEEE Engineering International Research Conference, EIRCON 2021
Country/Territory	Peru
City	Virtual, Lima
Period	27/10/21 → 29/10/21

Bibliographical note

Publisher Copyright:
© 2021 IEEE.

Keywords

Conjugate gradient method
Nonconvex functions
Optimization problems
Quasiconvex functions

Access to Document

10.1109/EIRCON52903.2021.9613264

Cite this

Aguilar Mendoza, H. S., Papa Quiroz, E. A., & Cano Lengua, M. A. (2021). An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications. In Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021 (Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/EIRCON52903.2021.9613264

Aguilar Mendoza, Hans Steven ; Papa Quiroz, Erik Alex ; Cano Lengua, Miguel Angel. / An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications. Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021. Institute of Electrical and Electronics Engineers Inc., 2021. (Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021).

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abstract = "This paper aims to identify the current state of the art of the latest research related to Conjugate Gradient (CG) methods for unconstrained optimization through a systematic literature review according to the methodology proposed by Kitchenham and Charter, to answer the following research questions: Q1: In what research areas are the conjugate gradient method used? Q2: Can Dai-Yuan conjugate gradient algorithm be effectively applied in portfolio selection? Q3: Have conjugate gradient methods been used to develop large-scale numerical results? Q4: What conjugate gradient methods have been used to minimize quasiconvex or nonconvex functions? We obtain useful results to extend the applications of the CG methods, develop efficient algorithms, and continue studying theoretical convergence results. ",

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language = "Ingl{\'e}s",

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Aguilar Mendoza, HS, Papa Quiroz, EA & Cano Lengua, MA 2021, An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications. in Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021. Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021, Institute of Electrical and Electronics Engineers Inc., 2nd IEEE Engineering International Research Conference, EIRCON 2021, Virtual, Lima, Peru, 27/10/21. https://doi.org/10.1109/EIRCON52903.2021.9613264

An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications. / Aguilar Mendoza, Hans Steven; Papa Quiroz, Erik Alex; Cano Lengua, Miguel Angel.

Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021. Institute of Electrical and Electronics Engineers Inc., 2021. (Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021).

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

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N2 - This paper aims to identify the current state of the art of the latest research related to Conjugate Gradient (CG) methods for unconstrained optimization through a systematic literature review according to the methodology proposed by Kitchenham and Charter, to answer the following research questions: Q1: In what research areas are the conjugate gradient method used? Q2: Can Dai-Yuan conjugate gradient algorithm be effectively applied in portfolio selection? Q3: Have conjugate gradient methods been used to develop large-scale numerical results? Q4: What conjugate gradient methods have been used to minimize quasiconvex or nonconvex functions? We obtain useful results to extend the applications of the CG methods, develop efficient algorithms, and continue studying theoretical convergence results.

AB - This paper aims to identify the current state of the art of the latest research related to Conjugate Gradient (CG) methods for unconstrained optimization through a systematic literature review according to the methodology proposed by Kitchenham and Charter, to answer the following research questions: Q1: In what research areas are the conjugate gradient method used? Q2: Can Dai-Yuan conjugate gradient algorithm be effectively applied in portfolio selection? Q3: Have conjugate gradient methods been used to develop large-scale numerical results? Q4: What conjugate gradient methods have been used to minimize quasiconvex or nonconvex functions? We obtain useful results to extend the applications of the CG methods, develop efficient algorithms, and continue studying theoretical convergence results.

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KW - Nonconvex functions

KW - Optimization problems

KW - Quasiconvex functions

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Aguilar Mendoza HS, Papa Quiroz EA, Cano Lengua MA. An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications. In Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021. Institute of Electrical and Electronics Engineers Inc. 2021. (Proceedings of the 2021 IEEE Engineering International Research Conference, EIRCON 2021). doi: 10.1109/EIRCON52903.2021.9613264

An Overview on Conjugate Gradient Methods for Optimization, Extensions and Applications

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Keywords

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