OPTIMALITY CONDITIONS FOR APPROXIMATE SOLUTIONS OF VECTOR OPTIMIZATION PROBLEMS WITH VARIABLE ORDERING STRUCTURES

We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces. Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems. Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimization problems with variable ordering structures applying nonlinear separating functionals and Eke land's variational principle.