The Generated Assumption Principle for Zulfia Mapping

Global optimality of a stationary point is commonly obtained by imposing struc-tural assumptions such as convexity, invexity, or related generalized convexity condi-tions. This paper develops a different viewpoint based on Zulfia Mapping. Instead ofprescribing the required structural condition externally, we investigate whether it canbe generated through the decompositionZ(x, u) = η(x, u) + ∆(x, u),where η(x, u) denotes a directed component and ∆(x, u) a deviation or correction. Weformulate a Generated Assumption Principle in which the structural relation requiredfor sufficiency is induced by the mapping and combined with stationarity to obtainglobal optimality. Convexity, invexity, and the corresponding classical KKT sufficiencyframework arise as limiting cases. The paper provides a concise foundation for studyingsufficiency through generated structure.