A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems
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- handle: 10670/1.idgehn
- hal: hal-02351104
- doi: 10.1007/s10589-019-00139-0
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Multi-objective programming Proximal point method DC function Variational rationality Behavioral sciencesSujets proches
Social science Sciences, Social Human sciences Social studies Behavioral sciences Science, Mental Mental philosophy Mind Behavioral sciences Service of process Service of papers Abuse of process Process Functions, ConvexCiter ce document
Glaydston de Carvalho Bento et al., « A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems », HAL-SHS : économie et finance, ID : 10.1007/s10589-019-00139-0
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Résumé
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.