  In this paper we propose a linear scalarization proximal point algorithm for
solving arbitrary 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. Furthermore, if each
iteration minimize the proximal regularized function and the proximal
parameters converges to zero we prove the convergence to a weak Pareto
solution. In the continuously differentiable case, it is proved the global
convergence of the sequence to a Pareto critical point and we introduce an
inexact algorithm with the same convergence properties. We also analyze
particular cases of the algorithm obtained finite convergence to a Pareto
optimal point when the objective functions are convex and a sharp minimum
condition is satisfied.
