Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP

Junqiao Qiu; Weibing Li; Yunong Zhang; Senbo Fu; Hongzhou Tan

doi:10.1109/ICSAI.2014.7009256

Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP

Junqiao Qiu, Weibing Li, Yunong Zhang, Senbo Fu, Hongzhou Tan

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

8 Citations (Scopus)

Abstract

This paper presents and investigates two new numerical algorithms (i.e., E47 algorithm and 94LVI algorithm) for solving the quadratic programming (QP) problem subject to inequality and bound constraints. Such a constrained QP problem is firstly converted equivalently into a linear variational inequality (LVI), and then converted equivalently into a piecewise-linear projection equation (PLPE). The E47 and 94LVI algorithms are employed to solve the resultant PLPE, and thus the optimal numerical solution to the QP problem is obtained readily. In this paper, we analyze the computational complexities and present the global convergence of the E47 and 94LVI algorithms. Moreover, the numerical-experiment results of E47 and 94LVI algorithms (compared with those of the active set algorithm) illustrate the efficacy and superiority of the presented algorithms for solving such inequality-and-bound constrained QP problems. Such two numerical algorithms can thus be applied safely and successfully to the motion planning and control of redundant robot manipulators, e.g., a real redundant robot manipulator, PA10 and PUMA560 robot manipulators, as well as wheeled mobile manipulators.

Original language	English
Title of host publication	2014 2nd International Conference on Systems and Informatics, ICSAI 2014
Publisher	IEEE
Pages	39-44
ISBN (Print)	9781479954582
DOIs	https://doi.org/10.1109/ICSAI.2014.7009256
Publication status	Published - 13 Jan 2015
Externally published	Yes
Event	2014 2nd International Conference on Systems and Informatics, ICSAI 2014 - Shanghai, China Duration: 15 Nov 2014 → 17 Nov 2014

Conference

Conference	2014 2nd International Conference on Systems and Informatics, ICSAI 2014
Place	China
City	Shanghai
Period	15/11/14 → 17/11/14

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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@inproceedings{9240e7046f9f447293cc45fed3ea9961,

title = "Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP",

abstract = "This paper presents and investigates two new numerical algorithms (i.e., E47 algorithm and 94LVI algorithm) for solving the quadratic programming (QP) problem subject to inequality and bound constraints. Such a constrained QP problem is firstly converted equivalently into a linear variational inequality (LVI), and then converted equivalently into a piecewise-linear projection equation (PLPE). The E47 and 94LVI algorithms are employed to solve the resultant PLPE, and thus the optimal numerical solution to the QP problem is obtained readily. In this paper, we analyze the computational complexities and present the global convergence of the E47 and 94LVI algorithms. Moreover, the numerical-experiment results of E47 and 94LVI algorithms (compared with those of the active set algorithm) illustrate the efficacy and superiority of the presented algorithms for solving such inequality-and-bound constrained QP problems. Such two numerical algorithms can thus be applied safely and successfully to the motion planning and control of redundant robot manipulators, e.g., a real redundant robot manipulator, PA10 and PUMA560 robot manipulators, as well as wheeled mobile manipulators.",

author = "Junqiao Qiu and Weibing Li and Yunong Zhang and Senbo Fu and Hongzhou Tan",

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doi = "10.1109/ICSAI.2014.7009256",

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Qiu, J, Li, W, Zhang, Y, Fu, S & Tan, H 2015, Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP. in 2014 2nd International Conference on Systems and Informatics, ICSAI 2014., 7009256, IEEE, pp. 39-44, 2014 2nd International Conference on Systems and Informatics, ICSAI 2014, Shanghai, China, 15/11/14. https://doi.org/10.1109/ICSAI.2014.7009256

Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP. / Qiu, Junqiao; Li, Weibing; Zhang, Yunong et al.
2014 2nd International Conference on Systems and Informatics, ICSAI 2014. IEEE, 2015. p. 39-44 7009256.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

TY - GEN

T1 - Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP

AU - Qiu, Junqiao

AU - Li, Weibing

AU - Zhang, Yunong

AU - Fu, Senbo

AU - Tan, Hongzhou

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2015/1/13

Y1 - 2015/1/13

N2 - This paper presents and investigates two new numerical algorithms (i.e., E47 algorithm and 94LVI algorithm) for solving the quadratic programming (QP) problem subject to inequality and bound constraints. Such a constrained QP problem is firstly converted equivalently into a linear variational inequality (LVI), and then converted equivalently into a piecewise-linear projection equation (PLPE). The E47 and 94LVI algorithms are employed to solve the resultant PLPE, and thus the optimal numerical solution to the QP problem is obtained readily. In this paper, we analyze the computational complexities and present the global convergence of the E47 and 94LVI algorithms. Moreover, the numerical-experiment results of E47 and 94LVI algorithms (compared with those of the active set algorithm) illustrate the efficacy and superiority of the presented algorithms for solving such inequality-and-bound constrained QP problems. Such two numerical algorithms can thus be applied safely and successfully to the motion planning and control of redundant robot manipulators, e.g., a real redundant robot manipulator, PA10 and PUMA560 robot manipulators, as well as wheeled mobile manipulators.

AB - This paper presents and investigates two new numerical algorithms (i.e., E47 algorithm and 94LVI algorithm) for solving the quadratic programming (QP) problem subject to inequality and bound constraints. Such a constrained QP problem is firstly converted equivalently into a linear variational inequality (LVI), and then converted equivalently into a piecewise-linear projection equation (PLPE). The E47 and 94LVI algorithms are employed to solve the resultant PLPE, and thus the optimal numerical solution to the QP problem is obtained readily. In this paper, we analyze the computational complexities and present the global convergence of the E47 and 94LVI algorithms. Moreover, the numerical-experiment results of E47 and 94LVI algorithms (compared with those of the active set algorithm) illustrate the efficacy and superiority of the presented algorithms for solving such inequality-and-bound constrained QP problems. Such two numerical algorithms can thus be applied safely and successfully to the motion planning and control of redundant robot manipulators, e.g., a real redundant robot manipulator, PA10 and PUMA560 robot manipulators, as well as wheeled mobile manipulators.

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DO - 10.1109/ICSAI.2014.7009256

M3 - RGC 32 - Refereed conference paper (with host publication)

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BT - 2014 2nd International Conference on Systems and Informatics, ICSAI 2014

PB - IEEE

T2 - 2014 2nd International Conference on Systems and Informatics, ICSAI 2014

Y2 - 15 November 2014 through 17 November 2014

ER -

Two numerical algorithms and numerical experiments for efficiently solving inequality-and-bound constrained QP

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