Admissible Mapping Structures for Zulfia Invex Functions

We introduce admissible mapping structures as a framework for directional be-
havior based on a class of mappings
Z = {Zi(x, u)}i∈I ,
satisfying
f (x) − f (u) ≥ ∇f (u)T Zi(x, u).
This formulation extends directional concepts from single mappings to structured
classes, allowing regime-dependent admissible directions. The framework provides
a foundational basis for structured optimization models and related directional
systems.