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\(\chi\)-Optimal solution of single objective nonlinear optimization problem with uncertain parameters

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Abstract

This paper addresses nonlinear optimization problem whose parameters are uncertain and lie in closed intervals. A partial ordering is introduced to define closeness between two intervals as well as two interval vectors. Existence of the solution of the model is studied using this partial ordering in case of unconstrained as well as constrained optimization problem. A variant of goal programming technique is used to develop a methodology to derive the solution. The methodology is illustrated through a numerical example. A possible application in finance is provided.

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Acknowledgements

The authors are greatly indebted to the anonymous referees for valuable comments and remarks aimed at the improvement of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, 248007, India

    Mrinal Jana

  2. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Geetanjali Panda

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  1. Mrinal Jana
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  2. Geetanjali Panda
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Correspondence to Mrinal Jana.

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Jana, M., Panda, G. \(\chi\)-Optimal solution of single objective nonlinear optimization problem with uncertain parameters. OPSEARCH 55, 165–186 (2018). https://doi.org/10.1007/s12597-017-0312-y

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  • DOI: https://doi.org/10.1007/s12597-017-0312-y

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