A Class of Zulfia Programming via KKT Conditions Without Assumptions
Year: 2026
Type: article
Abstract: 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.
Author: Khan, Zulfiqar Ali
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213599385
FWCI:
Cites:
Cited by:
Related to: