This paper is concerned with two d.p. (difference of polyhedral convex functions) programming models, unconstrained and linearly constrained, in a finite-dimensional setting. We obtain exact formulae for the Frechet and Mordukhovich subdifferentials of a d.p. function. We establish optimality conditions via subdifferentials in the sense of convex analysis, of Frechet and of Mordukhovich, and describe their relationships. Existence and computation of descent and steepest descent directions for both the models are also studied.
['Nguyen Thi Van Hang', 'Nguyen Dong Yen']
On the Problem of Minimizing a Difference of Polyhedral Convex Functions Under Linear Constraints