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Characterizations and Generating Efficient Solutions to Interval Optimization Problems

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Optimization, Variational Analysis and Applications (IFSOVAA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 355))

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Abstract

In this study, we propose a method to obtain complete efficient solution sets of the optimization problems with interval-valued functions. The proposed method is based on the cone method for multiobjective optimization problems. Toward developing the method, a bi-objective characterization of efficient solutions to the problem under consideration is reported. In addition, we provide a saddle point characterization of efficient solutions to the problem with the help of a newly defined Lagrangian function. Finally, we provide an algorithmic implementation of the proposed method and support it with two numerical examples.

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Abbreviations

IVF:

Interval-valued function

IOP:

Interval optimization problem

ES:

Efficient solution

NS:

Nondominated solution

POS:

Pareto optimal solution

SP:

Saddle point

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Acknowledgements

The authors extend a sincere thanks to the reviewers for their valuable comments. Financial support through Early Career Research Award (ECR/2015/000467), Science and Engineering Research Board, Government of India, is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    Amit Kumar Debnath & Debdas Ghosh

Authors
  1. Amit Kumar Debnath
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  2. Debdas Ghosh
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Corresponding author

Correspondence to Debdas Ghosh .

Editor information

Editors and Affiliations

  1. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    Vivek Laha

  2. Institut de Mathématiques de Toulouse, Paul Sabatier University, Toulouse, France

    Pierre Maréchal

  3. Institute of Science, Banaras Hindu University, Varanasi, Uttar Pradesh, India

    S. K. Mishra

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Debnath, A.K., Ghosh, D. (2021). Characterizations and Generating Efficient Solutions to Interval Optimization Problems. In: Laha, V., Maréchal, P., Mishra, S.K. (eds) Optimization, Variational Analysis and Applications. IFSOVAA 2020. Springer Proceedings in Mathematics & Statistics, vol 355. Springer, Singapore. https://doi.org/10.1007/978-981-16-1819-2_7

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