A logarithmic‐quadratic proximal point scalarization method for multiobjective programming

We present a proximal point method to solve multiobjective programming problems based on the scalarization for maps. We build a family of convex scalar strict representations of a convex map F from R ⁿ to R ^m with respect to the lexicographic order on R ^m and we add a variant of the logarithmic‐quadratic regularization of Auslender, where the unconstrained variables in the domain of F are introduced in the quadratic term. The nonegative variables employed in the scalarization are placed in the logarithmic term. We show that the central trajectory of the scalarized problem is bounded and converges to a weak pareto solution of the multiobjective optimization problem.