TY - JOUR
T1 - A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization
AU - Papa Quiroz, Erik Alex
AU - Apolinário, Hellena Christina Fernandes
AU - Villacorta, Kely Diana
AU - Oliveira, Paulo Roberto
PY - 2019/12/1
Y1 - 2019/12/1
N2 - © 2019, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, we propose a linear scalarization proximal point algorithm for solving lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and, using the condition that the proximal parameters are bounded, we prove the convergence of the sequence generated by the algorithm and, when the objective functions are continuous, we prove the convergence to a generalized critical point of the problem. Furthermore, for the continuously differentiable case we introduce an inexact algorithm, which converges to a Pareto critical point.
AB - © 2019, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, we propose a linear scalarization proximal point algorithm for solving lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and, using the condition that the proximal parameters are bounded, we prove the convergence of the sequence generated by the algorithm and, when the objective functions are continuous, we prove the convergence to a generalized critical point of the problem. Furthermore, for the continuously differentiable case we introduce an inexact algorithm, which converges to a Pareto critical point.
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U2 - 10.1007/s10957-019-01582-z
DO - 10.1007/s10957-019-01582-z
M3 - Article
SN - 0022-3239
SP - 1028
EP - 1052
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
ER -