The third axiom of filling properties

Since its first appearance in 1983, the filled function method, which was initiated to solve global optimization problems, has developed very rapidly. From the results conducted by many scholars, the ideal filled function has at least two properties: parameter-free and continuously differentiable. S...

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Bibliographic Details
Published inExamples and counterexamples Vol. 8; p. 100192
Main Author Pandiya, Ridwan
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Elsevier
Subjects
Counterexample
Filled function
Global optimization
Parameter-free
Filled function
Global optimization
Parameter-free
Counterexample
Online AccessGet full text
ISSN2666-657X
2666-657X
DOI10.1016/j.exco.2025.100192

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Summary:Since its first appearance in 1983, the filled function method, which was initiated to solve global optimization problems, has developed very rapidly. From the results conducted by many scholars, the ideal filled function has at least two properties: parameter-free and continuously differentiable. Several researchers have attempted to provide filled functions with such properties that meet the three axioms (filling properties) required by the filled function definition. The third axiom specifically states that the filled function has a minimum point in the region of attraction. This paper examines the fact that the currently available continuously differentiable parameter-free filled functions do not fulfil the third axiom of the filling properties by providing several counterexamples.
ISSN:2666-657X
2666-657X
DOI:10.1016/j.exco.2025.100192