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An Iterative Algorithm for the Nonlinear MC 2 Model with Variational Inequality Method

Author

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  • Chao Min

    (School of Science, Southwest Petroleum University, Chengdu 610500, China
    Institute for Artificial Intellegence, Southwest Petroleum University, Chengdu 610500, China)

  • Feifei Fan

    (School of Science, Southwest Petroleum University, Chengdu 610500, China)

  • Zhaozhong Yang

    (State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China)

  • Xiaogang Li

    (State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China)

Abstract

The multiple criteria and multiple constraint level (MC 2 ) model is a useful tool to deal with the decision programming problems, which concern multiple decision makers and uncertain resource constraint levels. In this paper, by regarding the nonlinear MC 2 problems as a class of mixed implicit variational inequalities, we develop an iterative algorithm to solve the nonlinear MC 2 problems through the resolvent operator technique. The convergence of the generated iterative sequence is analyzed and discussed by a calculation example, and the stability of Algorithm 1 is also verified by error propagation. By comparing with two other MC 2 -algorithms, Algorithm 1 performs well in terms of number of iterations and computation complexity.

Suggested Citation

  • Chao Min & Feifei Fan & Zhaozhong Yang & Xiaogang Li, 2019. "An Iterative Algorithm for the Nonlinear MC 2 Model with Variational Inequality Method," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:514-:d:237492
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    References listed on IDEAS

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    1. Toyasaki, Fuminori & Daniele, Patrizia & Wakolbinger, Tina, 2014. "A variational inequality formulation of equilibrium models for end-of-life products with nonlinear constraints," European Journal of Operational Research, Elsevier, vol. 236(1), pages 340-350.
    2. Diemuodeke, E.O. & Addo, A. & Oko, C.O.C. & Mulugetta, Y. & Ojapah, M.M., 2019. "Optimal mapping of hybrid renewable energy systems for locations using multi-criteria decision-making algorithm," Renewable Energy, Elsevier, vol. 134(C), pages 461-477.
    3. M. Gonçalves & J. Melo & L. Prudente, 2015. "Augmented Lagrangian methods for nonlinear programming with possible infeasibility," Journal of Global Optimization, Springer, vol. 63(2), pages 297-318, October.
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