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Radius of Robust Global Error Bound for Piecewise Linear Inequality Systems

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  • Thai Doan Chuong

    (Ton Duc Thang University
    Ton Duc Thang University)

Abstract

In this paper, we consider a subclass of uncertain convex inequality systems, called a class of uncertain piecewise linear systems, where the involved functions are piecewise linear. We define a concept of radius of robust global error bound for the piecewise linear inequality system under polytope uncertainty and provide formulas for calculating the radius of robust global error bound. This is achieved by employing a dual characterization for the existence of a robust global error bound of the uncertain piecewise linear system with polytope uncertainty.

Suggested Citation

  • Thai Doan Chuong, 2021. "Radius of Robust Global Error Bound for Piecewise Linear Inequality Systems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 68-82, October.
    • Handle: RePEc:spr:joptap:v:191:y:2021:i:1:d:10.1007_s10957-021-01924-w
    DOI: 10.1007/s10957-021-01924-w
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    References listed on IDEAS

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    1. T. D. Chuong & V. Jeyakumar, 2017. "An Exact Formula for Radius of Robust Feasibility of Uncertain Linear Programs," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 203-226, April.
    2. Jiawei Chen & Jun Li & Xiaobing Li & Yibing Lv & Jen-Chih Yao, 2020. "Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 384-399, February.
    3. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2015. "Robust solutions to multi-objective linear programs with uncertain data," European Journal of Operational Research, Elsevier, vol. 242(3), pages 730-743.
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