Multiobjective Problems: Enhanced Necessary Conditions and New Constraint Qualifications through Convexificators

ABSTRACT

In this paper, we study necessary optimality conditions for local Pareto and weak Pareto solutions of multiobjective problems involving inequality and equality constraints in terms of convexificators. We develop the enhanced Karush–Kuhn–Tucker conditions and introduce the associated pseudonormality and quasinormality conditions. We also introduce several other new constraint qualifications which entirely depend on the feasible set. Then a connecting link between these constraint qualifications is presented. Moreover, we provide several examples that clarify the interrelations between the different results that we have established.

KEYWORDS:

• Constraint qualification
• convexificator
• multiobjective optimization problem
• necessary optimality condition
• nonsmooth analysis
• pseudo-differential

AMS SUBJECT CLASSIFICATION:

• 49J52
• 90C29
• 90C46