Approximate weak optimality conditions in multiobjective generalized Nash equilibrium problems (Q6551760)

The authors consider multi-objective generalized Nash equilibrium problems, starting from the remark that the application of optimality conditions in the context of this type of problems with many objectives has not been investigated using approximate Karush-Kuhn-Tucker optimality conditions. The authors approach this issue starting by introducing the approximate Karush-Kuhn-Tucker optimality conditions for weak efficient solutions of multi-objective generalized Nash equilibrium problems. It is proved that every weak efficient solution meets the standard-approximate Karush-Kuhn-Tucker condition for multi-objective generalized Nash equilibrium problems. All the same, it is shown that these conditions impose excessive constraints for an algorithm to generate correspondence sequences. To address this point, the authors propose a new set of approximate weak Karush-Kuhn-Tucker conditions, specific to multi-objective generalized Nash equilibrium problems, showing their convergence towards weak Karush-Kuhn-Tucker points provided a cone-continuity property is satisfied. An augmented Lagrangian-type algorithm for multi-objective generalized Nash equilibrium problems is described for estimating an approximate weak Karush-Kuhn-Tucker optimality for this type of problems, also presenting a convergence analysis under the cone continuity conditions proved in this paper.