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semi-infinite programming, multi-objective fractional programming, invexInfinitely many equality and inequality constraints, parametric sufficient efficiency conditions

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First a new notion of the random exponential Hanson–Antczak type (α, β, ν, ε, η, ρ, h(∙,∙,∙), θ)-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function h(∙,∙,∙) of the second order is defined, and finally a class of asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming is established. Furthermore, several sets of asymptotic sufficiency results in which various generalized exponential type HA(α, β, γ, ε, η, ρ, h(∙,∙,∙), θ)-V-invexity assumptions are imposed on certain vector functions whose components are the individual as well as some combinations of the problem functions are examined and proved. To the best of our knowledge, all the established results on the semi-infinite aspects of the multi-objective fractional programming are new, which is a significantly new emerging field of the interdisciplinary research in nature. We also observed that the investigated results can be modified and applied to several special classes of nonlinear programming problems.

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SpringerPlus, v. 5, art. 1476