An inertial projection neural network for solving variational inequalities

Xing He; Tingwen Huang; Junzhi Yu; Chuandong Li; Chaojie Li

doi:10.1109/TCYB.2016.2523541

An inertial projection neural network for solving variational inequalities

Xing He
, Tingwen Huang
, Junzhi Yu
, Chuandong Li
, Chaojie Li

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

117 Citations (Scopus)

Abstract

Recently, projection neural network (PNN) was proposed for solving monotone variational inequalities (VIs) and related convex optimization problems. In this paper, considering the inertial term into first order PNNs, an inertial PNN (IPNN) is also proposed for solving VIs. Under certain conditions, the IPNN is proved to be stable, and can be applied to solve a broader class of constrained optimization problems related to VIs. Compared with existing neural networks (NNs), the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different Karush-Kuhn-Tucker optimal solution for nonconvex optimization problems. Finally, simulation results on three numerical examples show the effectiveness and performance of the proposed NN. © 2013 IEEE.

Original language	English
Article number	7404251
Pages (from-to)	809-814
Journal	IEEE Transactions on Cybernetics
Volume	47
Issue number	3
DOIs	https://doi.org/10.1109/TCYB.2016.2523541
Publication status	Published - 1 Mar 2017
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 Natural Science Foundation of China under Grant 61403313, Grant 61374078, and Grant 61375102, in part by the Natural Science Foundation Project of Chongqing CSTC under Grant cstc2014jcyjA40014, and 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.

Research Keywords

Inertial projection neural network (IPNN)
variational inequalities (VIs)

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title = "An inertial projection neural network for solving variational inequalities",

abstract = "Recently, projection neural network (PNN) was proposed for solving monotone variational inequalities (VIs) and related convex optimization problems. In this paper, considering the inertial term into first order PNNs, an inertial PNN (IPNN) is also proposed for solving VIs. Under certain conditions, the IPNN is proved to be stable, and can be applied to solve a broader class of constrained optimization problems related to VIs. Compared with existing neural networks (NNs), the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different Karush-Kuhn-Tucker optimal solution for nonconvex optimization problems. Finally, simulation results on three numerical examples show the effectiveness and performance of the proposed NN. {\textcopyright} 2013 IEEE.",

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AU - Huang, Tingwen

AU - Yu, Junzhi

AU - Li, Chuandong

AU - Li, Chaojie

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].

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N2 - Recently, projection neural network (PNN) was proposed for solving monotone variational inequalities (VIs) and related convex optimization problems. In this paper, considering the inertial term into first order PNNs, an inertial PNN (IPNN) is also proposed for solving VIs. Under certain conditions, the IPNN is proved to be stable, and can be applied to solve a broader class of constrained optimization problems related to VIs. Compared with existing neural networks (NNs), the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different Karush-Kuhn-Tucker optimal solution for nonconvex optimization problems. Finally, simulation results on three numerical examples show the effectiveness and performance of the proposed NN. © 2013 IEEE.

AB - Recently, projection neural network (PNN) was proposed for solving monotone variational inequalities (VIs) and related convex optimization problems. In this paper, considering the inertial term into first order PNNs, an inertial PNN (IPNN) is also proposed for solving VIs. Under certain conditions, the IPNN is proved to be stable, and can be applied to solve a broader class of constrained optimization problems related to VIs. Compared with existing neural networks (NNs), the presence of the inertial term allows us to overcome some drawbacks of many NNs, which are constructed based on the steepest descent method, and this model is more convenient for exploring different Karush-Kuhn-Tucker optimal solution for nonconvex optimization problems. Finally, simulation results on three numerical examples show the effectiveness and performance of the proposed NN. © 2013 IEEE.

KW - Inertial projection neural network (IPNN)

KW - variational inequalities (VIs)

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DO - 10.1109/TCYB.2016.2523541

M3 - RGC 21 - Publication in refereed journal

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SN - 2168-2267

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SP - 809

EP - 814

JO - IEEE Transactions on Cybernetics

JF - IEEE Transactions on Cybernetics

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ER -

An inertial projection neural network for solving variational inequalities

Abstract

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