Zulfiability and Zulfia-KKT Sufficiency: A Framework for Generated Optimality

We introduce Zulfiability, a new generalization of convexity via Zulfia Decompo-sition Mapping y − x = η(x, y) + r(x, y) and a correction map ∆(x, y). A functionf is said to be Zulfiable if f (y) − f (x) ≥ ∇f (x)T η(x, y) + ∆(x, y) with ∆(x, x) = 0.Based on this, we define Zulfia-KKT (ZKKT) Sufficiency Conditions for con-strained optimization with coupled corrections ∆f , ∆g, ∆h. We prove that ZKKT issufficient for global optimality without requiring convexity, LICQ, or a feasible startingpoint. Optimality is generated even from an infeasible x0. We show that when ∆ ≡ 0and η(x, y) = y − x, Zulfiability reduces to classical KKT, invexity, and Karmarkar’sinterior-point logic. Thus KKT, invexity and Karmarkar IPM are contained withinZulfiability. This establishes the principle of Generated Optimality.