Fréchet $$σ $$-subdifferential calculus rules and applications - Alizadeh, Mohammad Hossein; Zanjani, Alireza Youhannaee (Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2025)
We generalize the sum, difference, product, and chain rules for Fréchet σ-subdifferential. Also, we establish necessary optimality conditions for difference problems in terms of the σ-subdifferential. Our generalizations resemble the results by Mordukhovich, Nam, and Yen (Optimization 55 (2006) 685–708) regarding Fréchet σ-subdifferential.