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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| Veröffentlicht in: | Computational optimization and applications 2020, Vol.75 (1), p.263-290 |
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| creator | de Carvalho Bento, Glaydston Bitar, Sandro Dimy Barbosa da Cruz Neto, João Xavier Soubeyran, Antoine de Oliveira Souza, João Carlos |
| description | 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. |
| doi_str_mv | 10.1007/s10589-019-00139-0 |
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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. 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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. 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proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems</title><author>de Carvalho Bento, Glaydston ; Bitar, Sandro Dimy Barbosa ; da Cruz Neto, João Xavier ; Soubeyran, Antoine ; de Oliveira Souza, João Carlos</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c397t-f7f48bcde7f4fdef40a24c597895af88c5da23a5cfdbb7fa8e527d92c2a934573</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Ascent</topic><topic>Convex analysis</topic><topic>Convex and Discrete Geometry</topic><topic>Critical point</topic><topic>Economics and Finance</topic><topic>Goal programming</topic><topic>Group dynamics</topic><topic>Humanities and Social Sciences</topic><topic>Iterative methods</topic><topic>Management Science</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and 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| subjects | 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 Mathematics, Applied Multiple objective analysis Operations Research Operations Research & Management Science Operations Research/Decision Theory Optimization Pareto optimization Physical Sciences Science & Technology Statistics Technology |
| title | A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems |
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