5 research outputs found
On Computing the Mordukhovich Subdifferential Using Directed Sets in Two Dimensions
The Mordukhovich subdifferential is highly important in the variational and non-smooth analysis and
optimization, but it may often be hard to calculate it. Here we propose a method of computing the Mordukhovich
subdifferential of differences of sublinear (DS) functions applying the directed subdifferential of differences of
convex (DC) functions. We restrict ourselves to the two-dimensional case mainly for simplicity of the proofs and
for the visualizations.
The equivalence of the Mordukhovich symmetric subdifferential (the union of the corresponding subdifferential
and superdifferential), to the Rubinov subdifferential (the visualization of the directed subdifferential), is
established for DS functions in two dimensions. The Mordukhovich subdifferential and superdifferential are identified
as parts of the Rubinov subdifferential. In addition it is possible to construct the directed subdifferential in
a way similar to the Mordukhovich one by considering outer limits of Frechet subdifferentials. The results are
extended to the case of DC functions. Examples illustrating the obtained results are presented