Linear scalarization techniques for deriving optimality criteria of quasi-proper solutions in vector optimization with variable polyhedral orders

This study establishes optimality conditions for two classes of solutions in vector optimization problems: Ch-quasi proper non-dominated points and Ch-quasi proper minimal points. These solutions are analysed within a variable ordering structure induced by polyhedral cones, which play a crucial role in modelling constrained multiobjective problems. The proposed approach employs a linear scalarization technique under convexity-type assumptions, including cone-convexity of the vector objective and convexity of the constraint functions. A key contribution of this work is the explicit formulation of the scalarizing functional, which is constructed using a polyhedral dilating cone derived from the ordering cone. This formulation extends classical scalarization theory to the setting of point-dependent polyhedral domination, offering a theoretically tractable pathway for characterizing quasi-proper solutions. The results lay the analytical foundation for future algorithmic development leveraging the facial structure of polyhedral cones.