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<p>In this paper, we propose a class of proximal neurodynamic models (PNDMs) for solving mixed equilibrium problems (MEPs) in Hilbert spaces. Unlike existing approaches focused on variational inequalities and standard equilibrium problems, the proposed framework is specifically developed for MEPs and unifies finite-time (FT), fixed-time (FXT), and predefined-time (PdT) convergence through three distinct models. Under strong pseudomonotonicity and Lipschitz-type conditions, existence and uniqueness of the solution are established. Using Lyapunov techniques and proximal operator theory, explicit convergence conditions are derived for each model. In particular, the PdT model guarantees convergence within a user-prescribed time independent of initial conditions, while the FT and FXT models ensure initial-dependent and uniformly bounded convergence, respectively. The PdT model also exhibits faster convergence compared to its counterparts. The proposed framework is further applied to composite and minimax optimization problems using the FXT model, and to sparse signal recovery (SSR) using the PdT model. Numerical experiments validate the theoretical results and demonstrate the effectiveness and improved convergence performance of the proposed methods.</p>

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Stability analysis of neurodynamic approaches for solving strongly pseudomonotone mixed equilibrium problems and applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月29日

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  • Qian Wen,
  • Vajahat Karim Khan,
  • Qing-Bo Cai,
  • Md. Kalimuddin Ahmad

摘要

In this paper, we propose a class of proximal neurodynamic models (PNDMs) for solving mixed equilibrium problems (MEPs) in Hilbert spaces. Unlike existing approaches focused on variational inequalities and standard equilibrium problems, the proposed framework is specifically developed for MEPs and unifies finite-time (FT), fixed-time (FXT), and predefined-time (PdT) convergence through three distinct models. Under strong pseudomonotonicity and Lipschitz-type conditions, existence and uniqueness of the solution are established. Using Lyapunov techniques and proximal operator theory, explicit convergence conditions are derived for each model. In particular, the PdT model guarantees convergence within a user-prescribed time independent of initial conditions, while the FT and FXT models ensure initial-dependent and uniformly bounded convergence, respectively. The PdT model also exhibits faster convergence compared to its counterparts. The proposed framework is further applied to composite and minimax optimization problems using the FXT model, and to sparse signal recovery (SSR) using the PdT model. Numerical experiments validate the theoretical results and demonstrate the effectiveness and improved convergence performance of the proposed methods.