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
N1 - Publisher Copyright:
© 2019, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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 - 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.
KW - Fejér convergence
KW - Lower semicontinuous quasiconvex functions
KW - Multiobjective minimization
KW - Pareto–Clarke critical point
KW - Proximal point methods
UR - http://www.scopus.com/inward/record.url?scp=85073969071&partnerID=8YFLogxK
U2 - 10.1007/s10957-019-01582-z
DO - 10.1007/s10957-019-01582-z
M3 - Artículo
AN - SCOPUS:85073969071
SN - 0022-3239
VL - 183
SP - 1028
EP - 1052
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -