Role of exponential type random invexities for asymptotically sufficient efficiency conditions in semi-infinite multi-objective fractional programming.

Ram U Verma,Youngsoo Seol

doi:10.1186/s40064-016-3163-8

Abstract

First a new notion of the random exponential Hanson–Antczak type (alpha ,beta ,gamma ,xi ,eta ,rho ,h(cdot ,cdot ,cdot ),theta )-V-invexity is introduced, which generalizes most of the existing notions in the literature, second a random function h(cdot ,cdot ,cdot ) 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(alpha ,beta ,gamma ,xi ,eta ,rho ,h(cdot ,cdot ,cdot ),theta )-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.

Highlights

Based on the work of Antczak (2005) on the V-r-invex functions, Zalmai (2013a) generalized and investigated some multi-parameter generalizations of the parametrically sufficient efficiency results under various Hanson–Antczak-type generalized (α, β, γ, ξ, ρ, θ )-V-invexity assumptions for the semi-infinite multi-objective fractional programming problems
We plan to introduce the new notion of the random exponential Hanson–Antczak type (α, β, γ, ξ, η, ρ, h(·, ·, ·), θ )-V-invexity, which generalizes most of the existing notions in the literature, and establish some results on random function h(·, ·, ·) to the context of a class of asymptotically sufficient efficiency conditions in semiinfinite multi-objective fractional programming
We consider the following semi-infinite multi-objective fractional programming problem based on the random exponential type HA(α, β, γ, ξ, η, ρ, h(·, ·, ·), θ )-V-invexity: (P)

Summary

Introduction

Based on the work of Antczak (2005) on the V-r-invex functions, Zalmai (2013a) generalized and investigated some multi-parameter generalizations of the parametrically sufficient efficiency results under various Hanson–Antczak-type generalized (α, β, γ , ξ , ρ, θ )-V-invexity assumptions for the semi-infinite multi-objective fractional programming problems.

Results

Conclusion