Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Multiobjective programming
  • proximal point method
  • DC function
  • variational rationality
  • multiproduct firm

Mathematics Subject Classification

65K05, 65K10, 90C26, 47N10, 58E17

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Suggested citation

J. X. Cruz Neto, J. O. Lopes, R. V. G. Serra, J. C. O. Souza, A. Soubeyran. “A Boosted Proximal Point Method for Difference of Convex Functions in Multiobjective Optimization and the Growth of Multiproduct Firms.” Journal of Convex Analysis 33 (2026), No. 3&4, 817–840. https://doi.org/10.68381/jca33046

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.