A simplified single-parameter filled function method for unconstrained global optimization

To address the limitations of existing filled function methods—including complex multi-parameter tuning and ambiguous global-optimality verification—this paper proposes a simplified continuously differentiable filled function for unconstrained global optimization with only one interpretable parameter and no exponential or logarithmic terms. Under mild assumptions (continuous differentiability and coercivity of the objective function), we rigorously proved that the proposed function satisfies all essential axioms of a filled function, enabling explicit certification of global optimality. The resulting hybrid algorithm (SP-FFM) combines gradient-based local optimization with deterministic global search via grid sampling, requiring only a single grid-density parameter. This design eliminates the need for alternating between the original objective and auxiliary functions around local optima, significantly reducing computational effort and parameter-tuning complexity. Extensive numerical experiments on benchmark problems show that the algorithm converges to global minima within milliseconds, achieves a 100% success rate after grid refinement, and outperforms state-of-the-art methods in robustness and efficiency while maintaining insensitivity to initial points.