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On a class of fuzzy parametric variational inequality controlled differential equation problems in finite dimension spaces

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  • Heng-you Lan

    (Sichuan University of Science and Engineering)

Abstract

This work is motivated by the fact that very little is known about the fuzzy variational inequalities controlled differential equation problems in finite dimension real numeral spaces, which are studied more difficult than differential variational inequalities. It is interesting and challenging that how to solve the fuzzy variational inequalities in a fuzzy environment. The purpose of this paper is to introduce and study a class of new fuzzy parametric variational inequality controlled initial-value differential equation problems in finite dimensional Euclidean spaces. We establish existence of Carathéodory weak solutions for the fuzzy parametric variational inequality controlled initial-value differential equation problem under suitable conditions. Further, using method of centres with entropic regularization techniques and time-stepping methods, we emerge convergence analysis on iterative process for solving the initial-value differential fuzzy parametric inequalities. Finally, we give some open questions for our future research.

Suggested Citation

  • Heng-you Lan, 2019. "On a class of fuzzy parametric variational inequality controlled differential equation problems in finite dimension spaces," Fuzzy Optimization and Decision Making, Springer, vol. 18(3), pages 327-344, September.
    • Handle: RePEc:spr:fuzodm:v:18:y:2019:i:3:d:10.1007_s10700-018-9300-9
    DOI: 10.1007/s10700-018-9300-9
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    References listed on IDEAS

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    1. Xing Wang & Nan-Jing Huang, 2013. "Differential Vector Variational Inequalities in Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 109-129, July.
    2. Arvind Raghunathan & J. PÉRez-Correa & Eduardo Agosin & Lorenz Biegler, 2006. "Parameter estimation in metabolic flux balance models for batch fermentation—Formulation & Solution using Differential Variational Inequalities (DVIs)," Annals of Operations Research, Springer, vol. 148(1), pages 251-270, November.
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