Abstract
This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.
| Original language | English |
|---|---|
| Article number | 4545064 |
| Journal | Mathematical Problems in Engineering |
| Volume | 2019 |
| DOIs | |
| Publication status | Published - 2019 Jan 1 |
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ASJC Scopus subject areas
- Mathematics(all)
- Engineering(all)
Cite this
Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions. / Sun, Juhe; Wu, Xiao Ren; Saheya, B.; Chen, Jein Shan; Ko, Chun Hsu.
In: Mathematical Problems in Engineering, Vol. 2019, 4545064, 01.01.2019.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Neural Network for Solving SOCQP and SOCCVI Based on Two Discrete-Type Classes of SOC Complementarity Functions
AU - Sun, Juhe
AU - Wu, Xiao Ren
AU - Saheya, B.
AU - Chen, Jein Shan
AU - Ko, Chun Hsu
PY - 2019/1/1
Y1 - 2019/1/1
N2 - This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.
AB - This paper focuses on solving the quadratic programming problems with second-order cone constraints (SOCQP) and the second-order cone constrained variational inequality (SOCCVI) by using the neural network. More specifically, a neural network model based on two discrete-type families of SOC complementarity functions associated with second-order cone is proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of SOCQP and SOCCVI. The two discrete-type SOC complementarity functions are newly explored. The neural network uses the two discrete-type families of SOC complementarity functions to achieve two unconstrained minimizations which are the merit functions of the Karuch-Kuhn-Tucker equations for SOCQP and SOCCVI. We show that the merit functions for SOCQP and SOCCVI are Lyapunov functions and this neural network is asymptotically stable. The main contribution of this paper lies on its simulation part because we observe a different numerical performance from the existing one. In other words, for our two target problems, more effective SOC complementarity functions, which work well along with the proposed neural network, are discovered.
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U2 - 10.1155/2019/4545064
DO - 10.1155/2019/4545064
M3 - Article
AN - SCOPUS:85062259296
VL - 2019
JO - Mathematical Problems in Engineering
JF - Mathematical Problems in Engineering
SN - 1024-123X
M1 - 4545064
ER -