ε-Pareto Optimality Conditions for Convex Multiobjective Programming via Max Function

We consider a nondifferentiable convex multiobjective optimization problem whose feasible set is defined by affine equality constraints, convex inequality constraints, and an abstract convex set constraint. We obtain Fritz John and Kuhn–Tucker necessary and sufficient conditions for ε-Pareto optimality via a max function. We also provide some relations among ε-Pareto solutions for such a problem and approximate solutions for several associated scalar problems.

Keywords:

• Approximate solutions
• ε-Efficiency
• Max functions
• ε-Pareto optimality
• ε-Subdifferential

AMS Classification:

• 90C29
• 49M37