Approximative quasi-subdifferentials

Abstract

We introduce a kind of approximative quasi-subdifferential useful for the characterization of quasi-convex, lower semicontinuous functions. The relationship existing between this notion and some quasi-subdifferentials known in the literature is studied.

Keywords:

• Convex function
• Quasi-convex function
• Subdifferential
• Quasi-subdifferential
• Conjugation
• Normal cone

Keywords:

• Mathematics Subject Classifications: 2000
• 26A27
• 26B25

Acknowledgment

We thank the anonymous referees for their remarks, comments, and valuable suggestions.