On min-norm and min-max methods of multi-objective optimization

This paper examines Pareto optimality of solutions to multi-objective problems scalarized in the min-norm, compromise programming, generalized goal programming, or unrestricted min-max formulations. Issues addressed include, among others, uniqueness in solution or objective space, penalization for over-achievement of goals, min-max reformulation of goal programming, inferiority in Tchebycheff-norm minimization, strength and weakness of weighted-bound optimization, quasi-satisficing decision-making, just attaining or even over-passing the goals, trading off by modifying weights or goals, non-convex Pareto frontier. New general necessary and sufficient conditions for both Pareto optimality and weak Pareto optimality are presented. Various formulations are compared in theoretical performance with respect to the goal-point location. Ideas for advanced goal programming and interactive decision-making are introduced.