Admissible Mapping Structures for Zulfia Invex Functions

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