A Class of Zulfia Programming via KKT Conditions Without Assumptions

In classical optimization, convexity and invexity are widely used to ensure thatstationary points are globally optimal. In particular, invexity guarantees the suf-ficiency of Karush–Kuhn–Tucker (KKT) conditions through an inequality-basedframework. However, such conditions are typically imposed externally on the prob-lem.In this paper, we introduce a new class of mathematical programming problems,called Zulfia programming problems, based on the concept of Zulfia invexity [1],characterized by the inequalityZ(v) − Z(u) ≥ ∇Z(u)T η(v, u), ∀u, v.This framework preserves the invex-type structure while embedding it intrinsicallywithin the problem. We show that for this class, the KKT conditions are sufficientfor global optimality without requiring additional convexity or classical invexityassumptions. This establishes a new class of mathematical programming problemsin which optimality is an inherent property rather than an imposed condition.