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.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - © 2015, Springer Science+Business Media New York. 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 - © 2015, Springer Science+Business Media New York. 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).
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U2 - 10.1007/s10898-015-0367-3
DO - 10.1007/s10898-015-0367-3
M3 - Article
SN - 0925-5001
SP - 79
EP - 96
JO - Journal of Global Optimization
JF - Journal of Global Optimization
ER -