Pareto-Fenchel ε-Subdifferential Composition Rule and ε-Efficiency
Mounir El Maghri · Numerical Functional Analysis and Optimization · 2013
We are mainly concerned in this article with a first rule for the efficient (Pareto) ε-subdifferential concerning the composition of two convex vector mappings taking values in finite or infinite-dimensional pre-ordered spaces. The obtained formula is exact and holds under Moreau-Rockafellar or Attouch-Brézis qualification conditions. In fact, beyond regularity, the rule would not be accurate without convex (Fenchel) ε-subdifferential of one of the two composed mappings. But also, suitable fields of variation for vector parameters ε play crucial roles in the operation. These, moreover, really enable to derive for cone-constrained convex vector optimization problems, a complete ε-efficiency criterion of the Kuhn-Tucker type given in terms of a vector Lagrangian.