Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions

Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions

In this paper, a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow&g...

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Main Authors: Ramu Dubey, Lakshmi Narayan Mishra, Clemente Cesarano
Format: Article
Language:English
Published: MDPI AG 2019-08-01
Series:Axioms
Subjects:
symmetric duality
multiobjective
fractional programming
(<i>C</i>,<i>G<sub>f</sub></i>)-invexity
Online Access:https://www.mdpi.com/2075-1680/8/3/97
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spelling doaj-4fbbc8487fe2456593e00daa180f3be12020-11-25T01:12:12ZengMDPI AGAxioms2075-16802019-08-01839710.3390/axioms8030097axioms8030097Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity AssumptionsRamu Dubey0Lakshmi Narayan Mishra1Clemente Cesarano2Department of Mathematics, J.C. Bose University of Science and Technology, YMCA, Faridabad 121 006, IndiaDepartment of Mathematics, School of Advanced Sciences, Vellore Institute of Technology (VIT) University, Vellore 632 014, Tamil Nadu, IndiaSection of Mathematics, International Telematic University UNINETTUNO, C.so Vittorio Emanuele II, 3900186 Roma, ItalyIn this paper, a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>F</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity, <i>C</i>-convex etc.). We consider Mond&#8722;Weir type fractional symmetric dual programs and derive duality results under <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity assumptions. Our results generalize several known results in the literature.https://www.mdpi.com/2075-1680/8/3/97symmetric dualitymultiobjectivefractional programming(<i>C</i>,<i>G<sub>f</sub></i>)-invexity
collection DOAJ
language English
format Article
sources DOAJ
author Ramu Dubey
Lakshmi Narayan Mishra
Clemente Cesarano
spellingShingle Ramu Dubey
Lakshmi Narayan Mishra
Clemente Cesarano
Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions
Axioms
symmetric duality
multiobjective
fractional programming
(<i>C</i>,<i>G<sub>f</sub></i>)-invexity
author_facet Ramu Dubey
Lakshmi Narayan Mishra
Clemente Cesarano
author_sort Ramu Dubey
title Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions
title_short Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions
title_full Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions
title_fullStr Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions
title_full_unstemmed Multiobjective Fractional Symmetric Duality in Mathematical Programming with (<i>C</i>,<i>G<sub>f</sub></i>)-Invexity Assumptions
title_sort multiobjective fractional symmetric duality in mathematical programming with (<i>c</i>,<i>g<sub>f</sub></i>)-invexity assumptions
publisher MDPI AG
series Axioms
issn 2075-1680
publishDate 2019-08-01
description In this paper, a new class of <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invex functions introduce and give nontrivial numerical examples which justify exist such type of functions. Also, we construct generalized convexity definitions (such as, <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>F</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity, <i>C</i>-convex etc.). We consider Mond&#8722;Weir type fractional symmetric dual programs and derive duality results under <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>C</mi> <mo>,</mo> <msub> <mi>G</mi> <mi>f</mi> </msub> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>-invexity assumptions. Our results generalize several known results in the literature.
topic symmetric duality
multiobjective
fractional programming
(<i>C</i>,<i>G<sub>f</sub></i>)-invexity
url https://www.mdpi.com/2075-1680/8/3/97
work_keys_str_mv AT ramudubey multiobjectivefractionalsymmetricdualityinmathematicalprogrammingwithiciigsubfsubiinvexityassumptions
AT lakshminarayanmishra multiobjectivefractionalsymmetricdualityinmathematicalprogrammingwithiciigsubfsubiinvexityassumptions
AT clementecesarano multiobjectivefractionalsymmetricdualityinmathematicalprogrammingwithiciigsubfsubiinvexityassumptions
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