Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps

Abstract EN

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.