TY - JOUR
T1 - A scalarization proximal point method for quasiconvex multiobjective minimization
AU - Apolinário, H. C.F.
AU - Papa Quiroz, E. A.
AU - Oliveira, P. R.
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for nonconvex case, of the inexact proximal method for multiobjective convex minimization problems studied by Bonnel et al. (SIAM J Optim 15(4):953–970, 2005).
AB - In this paper we propose a scalarization proximal point method to solve multiobjective unconstrained minimization problems with locally Lipschitz and quasiconvex vector functions. We prove, under natural assumptions, that the sequence generated by the method is well defined and converges globally to a Pareto-Clarke critical point. Our method may be seen as an extension, for nonconvex case, of the inexact proximal method for multiobjective convex minimization problems studied by Bonnel et al. (SIAM J Optim 15(4):953–970, 2005).
KW - Clarke subdifferential
KW - Fejér convergence
KW - Multiobjective minimization
KW - Pareto-Clarke critical point
KW - Proximal point methods
KW - Quasiconvex functions
UR - http://www.scopus.com/inward/record.url?scp=84952716031&partnerID=8YFLogxK
U2 - 10.1007/s10898-015-0367-3
DO - 10.1007/s10898-015-0367-3
M3 - Artículo
AN - SCOPUS:84952716031
SN - 0925-5001
VL - 64
SP - 79
EP - 96
JO - Journal of Global Optimization
JF - Journal of Global Optimization
IS - 1
ER -