A critical view on invexity

TL;DR

This paper critically examines the literature on invexity, highlighting issues such as unclear definitions, trivial statements, incorrect proofs, and unprofessional responses, attributing these problems to a lack of community criticism.

Contribution

It provides a critical review of invexity research, emphasizing the need for clearer standards and more rigorous peer review in the field.

Findings

Many papers lack clear definitions of invexity

Some proofs in the literature are incorrect or trivial

Authors sometimes respond unprofessionally to questions

Abstract

The aim of this note is to emphasize the fact that in many papers on invexity published in prestigious journals there are not clear definitions, trivial or not clear statements and wrong proofs. We also point out the unprofessional way of answering readers' questions by some authors. We think that this is caused mainly by the lack of criticism of the invexity community