The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.
"Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps." Abstr. Appl. Anal. 2013 (SI23) 1 - 9, 2013. https://doi.org/10.1155/2013/570918