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

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...

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Vydáno v:Computational optimization and applications Ročník 75; číslo 1; s. 263 - 290
Hlavní autoři: de Carvalho Bento, Glaydston, Bitar, Sandro Dimy Barbosa, da Cruz Neto, João Xavier, Soubeyran, Antoine, de Oliveira Souza, João Carlos
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.01.2020
Springer Nature B.V
Springer Verlag
Témata:
Ascent
Convex analysis
Convex and Discrete Geometry
Critical point
Economics and Finance
Goal programming
Group dynamics
Humanities and Social Sciences
Iterative methods
Management Science
Mathematical analysis
Mathematics
Mathematics and Statistics
Multiple objective analysis
Operations Research
Operations Research/Decision Theory
Optimization
Pareto optimization
Statistics
Multi-objective programming
Behavioral sciences
Proximal point method
DC function
Variational rationality
ISSN:0926-6003, 1573-2894
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Shrnutí: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.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-019-00139-0