劉怡彤 穆學文

本文提出了一個神經(jīng)網(wǎng)絡(luò)算法，以求解二階錐變分不等式 （SOCCVI） 問題. 該算法利用一個光滑化Fischer-Burmeister（FB）函數(shù)處理問題對應(yīng)的KKT條件，將其轉(zhuǎn)化為一個無約束優(yōu)化問題. 利用Lyapunov方法本文證明，在給定的條件下，該神經(jīng)網(wǎng)絡(luò)Lyapunov穩(wěn)定，漸近穩(wěn)定且指數(shù)穩(wěn)定.數(shù)值模擬驗證了該神經(jīng)網(wǎng)絡(luò)的運算效果.

神經(jīng)網(wǎng)絡(luò)； 二階錐； Fischer-Burmeister函數(shù)； Lyapunov穩(wěn)定

O224A2023.011002

A neural network for solving the second-order cone constrained variational inequality problems

LIU Yi-Tong， MU Xue-Wen

（School of Mathematics and Statistics， Xidian University， Xian 710126， China）

A neural network is proposed to solve the second-order cone constrained variational inequality （SOCCVI） problems. In this method， a smoothed Fischer-Burmeister （FB） function is used? to deal with the KKT conditions corresponding to the problem， and then the KKT conditions are further transformed to an unconstrained optimization problem. The Lyapunov method is applied to show the Lyapunov stability， asymptotic stability and exponential stability of the neural network under given conditions. The effectiveness of the neural network is verified by numerical experiment.

Neural network； Second-order cone； Fischer-Burmeister function； Lyapunov stability

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