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

Abstract

We investigate the pointwise well-posedness of optimization
problems for locally convex cone-valued 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.