An interior proximal method in vector optimization

This paper studies the vector optimization problem of finding weakly efficient points for maps from RnRn to RmRm, with respect to the partial order induced by a closed, convex, and pointed cone C⊂RmC⊂Rm, with nonempty interior. We develop for this problem an extension of the proximal point method for scalar-valued convex optimization problem with a modified convergence sensing condition that allows us to construct an interior proximal method for solving VOP on nonpolyhedral set.

► We find weakly efficient points for a vector optimization problem, with respect to the partial order induced by a closed, convex, and pointed cone. ► We develop for this problem an extension of the proximal point method for scalar-valued convex optimization problem. ► We modify convergence sensing condition to construct an interior proximal method for solving POV on nonpolyhedral set.