A logarithmic-quadratic proximal point scalarization method for multiobjective programming

We present a proximal point method to solve multiobjective problems based on the scalarization for maps. We build a family of a convex scalar strict representation of a convex map F with respect to the lexicographic order on R and we add a variant of the logarithmquadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced on the quadratic term and the constrained variables employed in the scalarization we put on the logarithmic term. We show that the central trajectory of the scalarized problem is bounded and converges to a weak Pareto of the multiobjective problem .