Logarithmic quasi-distance proximal point scalarization method for multi-objective programming

Recently, Gregório and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this study, a variation of this method is proposed, using the regularization with logarithm and quasi-distance. By restricting it to a certain class of quasi-distances that are Lipschitz continuous and coercive in any of their arguments, we show that any sequence {(xk,zk)}⊂Rn×R++m generated by the method satisfies: {zk} is convergent; and {xk} is bounded and its accumulation points are weak Pareto solutions of the unconstrained multi-objective optimization problem