A proximal neurodynamic model for solving inverse mixed variational inequalities.
Xingxing Ju1, Chuandong Li1, Xing He1
1Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, School of Electronic and Information Engineering, Southwest University, Chongqing 400715, China.
Summary
This study introduces a proximal neurodynamic model (PNDM) for solving inverse mixed variational inequalities (IMVIs). The PNDM demonstrates a unique continuous solution and stable equilibrium points, validated by numerical examples.
Area of Science:
- Optimization
- Applied Mathematics
- Computational Neuroscience
Background:
- Variational inequalities are fundamental in optimization and game theory.
- Solving inverse mixed variational inequalities (IMVIs) presents significant computational challenges.
- Existing models often lack guaranteed stability or convergence properties.
Purpose of the Study:
- To propose a novel proximal neurodynamic model (PNDM) for solving IMVIs.
- To analyze the theoretical properties of the PNDM, including solution uniqueness and stability.
- To demonstrate the practical effectiveness of the PNDM through numerical simulations.
Main Methods:
- Development of a PNDM utilizing the proximal operator.
- Mathematical analysis to establish conditions for a unique continuous solution (Lipschitz continuity).
- Stability analysis of the PNDM's equilibrium point (asymptotic and exponential stability).
Main Results:
- The PNDM guarantees a unique continuous solution under Lipschitz continuity conditions.
- The equilibrium point of the PNDM is proven to be asymptotically or exponentially stable.
- Numerical examples confirm the effectiveness and performance of the proposed PNDM.
Conclusions:
- The proximal neurodynamic model offers a robust framework for addressing IMVIs.
- The theoretical guarantees of solution uniqueness and stability enhance the model's reliability.
- The PNDM is a promising tool for various applications requiring the solution of IMVIs.
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