Pointwise well-posedness and scalarization of optimization problems for locally convex cone-valued functions

We investigate the pointwise well-posedness of optimization problems for locally convex conevalued functions and establish some relations between the kinds of well-posedness. Via the neighborhoods and elements, we define the scalarization functions for locally convex cones and discuss their properties. We consider the scalar optimization problems and obtain some results about the well-posedness of the optimization problems.