Invex functions and generalized convexity in multiobjective programming

Martin studied the optimality conditions of invex functions for scalar programming problems. In this work, we generalize his results making them applicable to vectorial optimization problems. We prove that the equivalence between minima and stationary points or Karush–Kuhn–Tucker points (depending on the case) remains true if we optimize several objective functions instead of one objective function. To this end, we define accurately stationary points and Karush–Kuhn–Tucker optimality conditions for multiobjective programming problems. We see that the Martin results cannot be improved in mathematical programming, because the new types of generalized convexity that have appeared over the last few years do not yield and any new optimality conditions for mathematical programming problems.