TY - JOUR
T1 - Inexact Proximal Point Methods for Multiobjective Quasiconvex Minimization on Hadamard Manifolds
AU - Papa Quiroz, Erik Alex
AU - Baygorrea Cusihuallpa, Nancy
AU - Maculan, Nelson
N1 - Publisher Copyright:
© 2020, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - In this paper, we present two inexact scalarization proximal point methods to solve quasiconvex multiobjective minimization problems on Hadamard manifolds. Under standard assumptions on the problem, we prove that the two sequences generated by the algorithms converge to a Pareto critical point of the problem and, for the convex case, the sequences converge to a weak Pareto solution. Finally, we explore an application of the method to demand theory in economy, which can be dealt with using the proposed algorithm.
AB - In this paper, we present two inexact scalarization proximal point methods to solve quasiconvex multiobjective minimization problems on Hadamard manifolds. Under standard assumptions on the problem, we prove that the two sequences generated by the algorithms converge to a Pareto critical point of the problem and, for the convex case, the sequences converge to a weak Pareto solution. Finally, we explore an application of the method to demand theory in economy, which can be dealt with using the proposed algorithm.
KW - Hadamard manifolds
KW - Multiobjective optimization
KW - Pareto optimality
KW - Proximal point methods
KW - Quasiconvex function
UR - http://www.scopus.com/inward/record.url?scp=85089012992&partnerID=8YFLogxK
U2 - 10.1007/s10957-020-01725-7
DO - 10.1007/s10957-020-01725-7
M3 - Article
AN - SCOPUS:85089012992
SN - 0022-3239
VL - 186
SP - 879
EP - 898
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -