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Necessary Optimality Condition for Nonlinear Interval Vector Programming Problem Under B-Arcwise Connected Functions

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications (WCGO 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 991))

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Abstract

We consider the nonlinear interval vector programming problem (NIVP) for solving uncertainty programming problems and introduced the set of B-arcwise connected interval-valued function (BCIF) and strictly BCIF (SBCIF) by generalizing the notion of arcwise connected interval-valued function. Arcwise connected function is a generalization of convex function which is defined on the arcwise connected set [2]. The differentiability of the function is studied by introducing right generalized Hukuhara derivative (gH-derivative or gH-differentiable). The extremum conditions for the functions under right gH-derivative have been derived. This is a new type of NIVP with right gH-differentiable function in both multiple objective and constraints involving BCIFs. The Fritz-John kind and Karush-Kuhn-Tucker kind necessary weakly LU-efficiency condition for NIVP are obtained with right gH-differentiable BCIFs in both multiple objective function and constraints functions.

The research of Mohan Bir Subba is supported by Council of Scientific and Industrial Research (CSIR), New Delhi, India through File No.: 09/1191(0001)/2017-EMR-I.

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Authors and Affiliations

  1. National Institute of Technology Mizoram, Chaltlang, Aizawl, 796012, Mizoram, India

    Mohan Bir Subba & Vinay Singh

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  1. Mohan Bir Subba
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  2. Vinay Singh
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Correspondence to Mohan Bir Subba .

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Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai An Le Thi

  2. Computer Science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen Normadie, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh

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Subba, M.B., Singh, V. (2020). Necessary Optimality Condition for Nonlinear Interval Vector Programming Problem Under B-Arcwise Connected Functions. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_65

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