A critical view on invexity (Q462990)

The concept of invexity was first introduced in the 1980s. The main focus of invexity is to find a class of functions for which any point where the derivative of a function vanishes, called critical point, is also a global minimum of the function. The aim of this note is to show that a number of publications on invexity in prestigious journals contain unclear definitions, ambiguous statements and sometimes wrong proofs. By analyzing certain facts of some relevant works, the author wishes to call the readers' attention to the literature on invexity when they use it in their research.