A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems

Glaydston de Carvalho Bento (1) , Sandro Dimy Barbosa Bitar (2) , João Xavier da Cruz Neto (3) , Antoine Soubeyran (4) , João Carlos de Oliveira Souza (5)

1 IME - IME, Federal University of Goiás
2 ICE - ICE, Federal University of Amazonas
3 CCN, DM, - CCN, DM, Federal University of Piauí
4 AMSE - Aix-Marseille Sciences Economiques
5 Federal University of Piauí

We consider the constrained multi-objective optimization problem of finding Pareto critical points of difference of convex functions. The new approach proposed by Bento et al. (SIAM J Optim 28:1104–1120, 2018) to study the convergence of the proximal point method is applied. Our method minimizes at each iteration a convex approximation instead of the (non-convex) objective function constrained to a possibly non-convex set which assures the vector improving process. The motivation comes from the famous Group Dynamic problem in Behavioral Sciences where, at each step, a group of (possible badly informed) agents tries to increase his joint payoff, in order to be able to increase the payoff of each of them. In this way, at each step, this ascent process guarantees the stability of the group. Some encouraging preliminary numerical results are reported.

Keywords: Multi-objective programming; Proximal point method; DC function; Variational rationality; Behavioral sciences

Domains: Humanities and Social Sciences; Economics and Finance

Glaydston de Carvalho Bento, Sandro Dimy Barbosa Bitar, João Xavier da Cruz Neto, Antoine Soubeyran, João Carlos de Oliveira Souza. A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems. Computational Optimization and Applications, 2020, 75 (1), pp.263-290. ⟨10.1007/s10589-019-00139-0⟩. ⟨hal-02351104⟩