Inflection point-based auxiliary function algorithm for finding global minima of coercive functions

Parameter-free filled functions have become a new direction for the auxiliary function approach development as parameters serve as the main barrier of the filled function's efficiency. However, the parameter-free filled function suffers from at least three shortcomings, namely, the use of an exponential function, a lower semi-continuous property, and the fulfillment of the third axiom of the filled function definition. This paper intends to address these limitations by providing a new inflection point-based auxiliary function. This function has continuously differentiable and non-exponential properties. To show the competitiveness of the proposed method, we conduct a comparison with some recently introduced filled function algorithms. Numerical results show the superiority of the proposed method