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Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative

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Abstract

This paper addresses the optimization problems with interval-valued objective function. For this we consider two types of order relation on the interval space. For each order relation, we obtain KKT conditions using of the concept of generalized Hukuhara derivative (\(gH\)-derivative) for interval-valued functions. The \(gH\)-derivative is a concept more general of derivative for this class of functions than other concepts of derivative. We make some comparison with previous result given by other authors and we show some advantages of our result.

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Acknowledgments

The research in this paper has been partially supported by Fondecyt-Chile through project 1120665, FAPESP—Brasil under the grant 2011/13985-0 and Ministerio de Ciencia e Innovación, Spain, through grant MTM2008-00018.

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Authors and Affiliations

  1. Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7D, Arica, Chile

    Y. Chalco-Cano

  2. Department of Mathematical and Statistical Sciences, University of Colorado, Denver, CO, 80217, USA

    W. A. Lodwick

  3. Dpto. de Estadística e I.O., Universidad de Sevilla, 41012 , Sevilla, Spain

    A. Rufian-Lizana

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  1. Y. Chalco-Cano
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  2. W. A. Lodwick
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  3. A. Rufian-Lizana
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Correspondence to Y. Chalco-Cano.

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Chalco-Cano, Y., Lodwick, W.A. & Rufian-Lizana, A. Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optim Decis Making 12, 305–322 (2013). https://doi.org/10.1007/s10700-013-9156-y

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