Second-order strong optimality and duality for nonsmooth multiobjective fractional programming with constraints - Chen J.; Liu L.; Lv Y.; Ghosh D.; Yao J.C. (My University, 2025)
This paper investigates nonsmooth multiobjective fractional programming (NMFP) with inequalities and equalities constraints in real reflexive Banach spaces. It derives a quotient calculus rule for computing the first- and second-order Clarke derivatives of fractional functions involving locally Lipschitz functions. A novel second-order Abadie-type regularity condition is presented, defined with the help of the Clarke directional derivative and the Páles–Zeidan second-order directional derivative. We establish both first- and second-order strong necessary optimality conditions, which contain some new information on multipliers and imply the strong KKT necessary conditions, for a Borwein-type properly efficient solution of NMFP by utilizing generalized directional derivatives. Moreover, it derives second-order sufficient optimality conditions for NMFP under a second-order generalized convexity assumption. Additionally, we derive duality results between NMFP and its second-order dual problem under some appropriate conditions © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.