Accelerated tensor-based conjugate gradient framework using modified secant condition for image restoration and strategic UAV combat

Navigating large-scale unconstrained optimization complexities requires a synergistic integration of the low memory footprint of conjugate gradient (CG) methods with the fast convergence of quasi-Newton (QN) methods. This paper proposes the Self-Accelerated Regularized Tensor-based BFGS (SAR-TBFGS) algorithm, a sophisticated framework that advances recent third-order tensor-based schemes. The algorithm incorporates three pivotal innovations: a self-acceleration mechanism for adaptive step modulation, a modified secant equation leveraging gradient and function value evolution, and an adaptive regularization parameter, formulated via Frobenius norm minimization, for enhanced numerical stability. Theoretical analysis confirms that SAR-TBFGS maintains the sufficient descent property and ensures global convergence under standard Wolfe conditions. Numerical evaluations via Dolan–Moré profiles demonstrate consistent superiority over state-of-the-art solvers in speed and accuracy. Finally, the algorithm’s practical utility is validated through salt-and-pepper image restoration and tactical decision-making in strategic multi-Unmanned Aerial Vehicle (UAV) air combat games.