Nonlinear Scalarization Functions and Well Posedness in Vector Optimization

A class of nonlinear scalarization functions is defined.DH-well posedness and B-well posedness of vector optimization problems with variable cone structure are given.By applying this nonlinear scalarization function,a vector optimization problem under variable cone structure is convert to a scalar optimization problem.Moreover,the relationships of well posedness between this class of scalar optimization problems and vector optimization problems with variable cone structure are studied.