Journal of Convex Analysis 33 (2026), No. 3&4, 817--840
Copyright Heldermann Verlag 2026
A Boosted Proximal Point Method for Difference of Convex Functions in Multiobjective Optimization and the Growth of Multiproduct Firms
Joao X. Cruz Neto
Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil
jxavier@ufpi.edu.br
Jurandir O. Lopes
Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil
jurandir@ufpi.edu.br
Ray V. G. Serra
Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil
rayserra@ufpi.edu.br
Antoine Soubeyran
Aix-Marseille University, School of Economics, CNRS & EHESS, Marseille, France
antoine.soubeyran@gmail.com
Joao C. O. Souza
Dept. of Mathematics, Federal University of Piauí, Teresina, Brazil
joaocos.mat@ufpi.edu.br
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.
Keywords: Multiobjective programming, proximal point method, DC function, variational rationality, multiproduct firm.
MSC: 65K05, 65K10, 90C26, 47N10, 58E17.
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