A Boosted Proximal Point Method for Difference of Convex Functions in Multiobjective Optimization and the Growth of Multiproduct Firms

This paper has two sides: a mathematical side and a behavioral side. In the first part, we consider the unconstrained multiobjective optimization problem of finding Pareto critical points of difference of convex functions. We study a method that minimizes at each iteration a convex approximation instead of the (non-convex) objective function constrained to a possible non-convex set which imposes the method decreases, at each step, each objective function. In the second part, as an application, we propose a variational rationality perspective to multiproduct firm problem that wants to improve progressively the profits of all its sub-units by adjusting their production levels. This approach is completly new in management sciences/economics. It opens the door to a variational rational theory of the multiproduct firm.