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In this paper we propose a scalarization proximal point method to solvemultiobjective unconstrained minimization problems with locally Lipschitz andquasiconvex vector functions. We prove, under natural assumptions, that thesequence generated by the method is well defined and converges globally to aPareto-Clarke critical point. Our method may be seen as an extension, for thenon convex case, of the inexact proximal method for multiobjective convexminimization problems studied by Bonnel et al. (SIAM Journal on Optimization15, 4, 953-970, 2005).

A Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization