A novel parameter-free differentiable filled function for global optimization

Area of Science:

• Optimization
• Numerical Analysis
• Computational Mathematics

Background:

• The filled function method is crucial for global optimization, addressing limitations of local minimizers.
• Existing filled functions often face challenges with non-differentiability or complex parameter tuning.
• Current research seeks parameter-free or differentiable variants, but structural simplicity and robustness remain difficult.

Purpose of the Study:

• To propose a novel filled function that is both parameter-free and continuously differentiable.
• To overcome the limitations of existing filled functions regarding parameter dependence and differentiability.
• To offer a more streamlined and computationally efficient tool for global optimization problems.

Main Methods:

• Development of a novel filled function formulation.
• Theoretical analysis to establish its filling properties.
• Numerical experiments on benchmark functions to evaluate performance.

Main Results:

• The proposed filled function is completely parameter-free and continuously differentiable.
• Theoretical analysis confirms its effective filling properties.
• Numerical results show superior convergence efficiency and reliability over existing methods.

Conclusions:

• The novel filled function offers a significant improvement in structural simplicity and numerical robustness.
• Elimination of parameter tuning and guaranteed smoothness enable direct use of gradient-based solvers.
• This contributes a more efficient and reliable tool for tackling global optimization challenges.