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Radius of Robust Feasibility of System of Convex Inequalities with Uncertain Data

Author

Listed:
  • Jiawei Chen

    (Southwest University)

  • Jun Li

    (Southwest University)

  • Xiaobing Li

    (Chongqing Jiaotong University)

  • Yibing Lv

    (Yangtze University)

  • Jen-Chih Yao

    (China Medical University)

Abstract

In this paper, we investigate the radius of robust feasibility of system of uncertain convex inequalities by the Minkowski function. We firstly establish an upper bound and a lower bound for radius of robust feasibility of the system of uncertain convex inequalities. Exact formulas of radius of robust feasibility of the system are derived under the nonsymmetric and symmetric assumptions of the uncertain sets. We also obtain a characterization on the positiveness of radius of robust feasibility for the system. Lastly, explicit tractable formulas for computing the radius of robust feasibility of the system are presented when the uncertain sets are ellipsoids, polytopes, boxes and unit ball, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:184:y:2020:i:2:d:10.1007_s10957-019-01607-7
    DOI: 10.1007/s10957-019-01607-7
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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 & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, May.
    3. A. L. Soyster, 1973. "Technical Note—Convex Programming with Set-Inclusive Constraints and Applications to Inexact Linear Programming," Operations Research, INFORMS, vol. 21(5), pages 1154-1157, October.
    4. V. Jeyakumar & G. M. Lee & G. Li, 2015. "Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 407-435, February.
    5. 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.
    6. Xin Chen & Yuhan Zhang, 2009. "Uncertain Linear Programs: Extended Affinely Adjustable Robust Counterparts," Operations Research, INFORMS, vol. 57(6), pages 1469-1482, December.
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    Cited by:

    1. 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.
    2. Xiangkai Sun & Kok Lay Teo & Xian-Jun Long, 2021. "Some Characterizations of Approximate Solutions for Robust Semi-infinite Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 281-310, October.
    3. Frauke Liers & Lars Schewe & Johannes Thürauf, 2022. "Radius of Robust Feasibility for Mixed-Integer Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 243-261, January.
    4. Jie Wang & Shengjie Li & Min Feng, 2022. "Unified Robust Necessary Optimality Conditions for Nonconvex Nonsmooth Uncertain Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 226-248, October.
    5. Jiawei Chen & Suliman Al-Homidan & Qamrul Hasan Ansari & Jun Li & Yibing Lv, 2021. "Robust Necessary Optimality Conditions for Nondifferentiable Complex Fractional Programming with Uncertain Data," Journal of Optimization Theory and Applications, Springer, vol. 189(1), pages 221-243, April.
    6. Xiangkai Sun & Wen Tan & Kok Lay Teo, 2023. "Characterizing a Class of Robust Vector Polynomial Optimization via Sum of Squares Conditions," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 737-764, May.
    7. M. A. Goberna & V. Jeyakumar & G. Li, 2021. "Calculating Radius of Robust Feasibility of Uncertain Linear Conic Programs via Semi-definite Programs," Journal of Optimization Theory and Applications, Springer, vol. 189(2), pages 597-622, May.
    8. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2022. "The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments," European Journal of Operational Research, Elsevier, vol. 296(3), pages 749-763.

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