A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach

Chaojie Li; Xinghuo Yu; Tingwen Huang; Guo Chen; Xing He

doi:10.1109/TNNLS.2015.2496658

A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach

Chaojie Li
, Xinghuo Yu
, Tingwen Huang
, Guo Chen
, Xing He

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

136 Citations (Scopus)

Abstract

This paper proposes a generalized Hopfield network for solving general constrained convex optimization problems. First, the existence and the uniqueness of solutions to the generalized Hopfield network in the Filippov sense are proved. Then, the Lie derivative is introduced to analyze the stability of the network using a differential inclusion. The optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced Fritz John conditions. The convergence rate of the generalized Hopfield network can be estimated by the second-order derivative of the energy function. The effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four-Tank benchmark. © 2012 IEEE.

Original language	English
Article number	7331294
Pages (from-to)	308-321
Journal	IEEE Transactions on Neural Networks and Learning Systems
Volume	27
Issue number	2
DOIs	https://doi.org/10.1109/TNNLS.2015.2496658
Publication status	Published - 1 Feb 2016
Externally published	Yes

Bibliographical note

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].

Funding

This work was supported in part by the National Priorities Research Program through the Qatar National Research Fund, a member of Qatar Foundation under Grant NPRP 4-1162-1-181, in part by the Fundamental Research Funds through the Australian Research Council Discovery Scheme under Grant 140100544, in part by the Fundamental Research Funds for Central Universities under Project XDJK2014C118, in part by the Natural Science Foundation of China under Grant 61403313, and in part by the Natural Science Foundation Project through the China Sustainable Transportation Center, Chongqing, under Grant cstc2014jcyjA40014.

Research Keywords

Constraints
enhanced Fritz John conditions
Filippov solutions
global optimization
Hopfield network
Lie derivative.

Access Output

10.1109/TNNLS.2015.2496658

Other Access Options

Check CityUHK Library

Permanent Link

Right click to copy link

Cite this

@article{d8db90be5ae04855ac3ff93411b330f4,

title = "A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach",

abstract = "This paper proposes a generalized Hopfield network for solving general constrained convex optimization problems. First, the existence and the uniqueness of solutions to the generalized Hopfield network in the Filippov sense are proved. Then, the Lie derivative is introduced to analyze the stability of the network using a differential inclusion. The optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced Fritz John conditions. The convergence rate of the generalized Hopfield network can be estimated by the second-order derivative of the energy function. The effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four-Tank benchmark. {\textcopyright} 2012 IEEE.",

keywords = "Constraints, enhanced Fritz John conditions, Filippov solutions, global optimization, Hopfield network, Lie derivative.",

author = "Chaojie Li and Xinghuo Yu and Tingwen Huang and Guo Chen and Xing He",

note = "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].",

year = "2016",

month = feb,

day = "1",

doi = "10.1109/TNNLS.2015.2496658",

language = "English",

volume = "27",

pages = "308--321",

journal = "IEEE Transactions on Neural Networks and Learning Systems",

issn = "2162-237X",

publisher = "IEEE Computational Intelligence Society",

number = "2",

}

A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach. / Li, Chaojie; Yu, Xinghuo; Huang, Tingwen et al.
In: IEEE Transactions on Neural Networks and Learning Systems, Vol. 27, No. 2, 7331294, 01.02.2016, p. 308-321.

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

TY - JOUR

T1 - A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization

T2 - Lie Derivative Approach

AU - Li, Chaojie

AU - Yu, Xinghuo

AU - Huang, Tingwen

AU - Chen, Guo

AU - He, Xing

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 - 2016/2/1

Y1 - 2016/2/1

N2 - This paper proposes a generalized Hopfield network for solving general constrained convex optimization problems. First, the existence and the uniqueness of solutions to the generalized Hopfield network in the Filippov sense are proved. Then, the Lie derivative is introduced to analyze the stability of the network using a differential inclusion. The optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced Fritz John conditions. The convergence rate of the generalized Hopfield network can be estimated by the second-order derivative of the energy function. The effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four-Tank benchmark. © 2012 IEEE.

AB - This paper proposes a generalized Hopfield network for solving general constrained convex optimization problems. First, the existence and the uniqueness of solutions to the generalized Hopfield network in the Filippov sense are proved. Then, the Lie derivative is introduced to analyze the stability of the network using a differential inclusion. The optimality of the solution to the nonsmooth constrained optimization problems is shown to be guaranteed by the enhanced Fritz John conditions. The convergence rate of the generalized Hopfield network can be estimated by the second-order derivative of the energy function. The effectiveness of the proposed network is evaluated on several typical nonsmooth optimization problems and used to solve the hierarchical and distributed model predictive control four-Tank benchmark. © 2012 IEEE.

KW - Constraints

KW - enhanced Fritz John conditions

KW - Filippov solutions

KW - global optimization

KW - Hopfield network

KW - Lie derivative.

UR - https://www.scopus.com/pages/publications/84947969693

UR - https://www.scopus.com/pages/publications/84947969693#tab=impact

U2 - 10.1109/TNNLS.2015.2496658

DO - 10.1109/TNNLS.2015.2496658

M3 - RGC 21 - Publication in refereed journal

SN - 2162-237X

VL - 27

SP - 308

EP - 321

JO - IEEE Transactions on Neural Networks and Learning Systems

JF - IEEE Transactions on Neural Networks and Learning Systems

IS - 2

M1 - 7331294

ER -

A Generalized Hopfield Network for Nonsmooth Constrained Convex Optimization: Lie Derivative Approach

Abstract

Bibliographical note

Funding

Research Keywords

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Cite this