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Some Characterizations of Approximate Solutions for Robust Semi-infinite Optimization Problems

Author

Listed:
  • Xiangkai Sun

    (Chongqing Technology and Business University)

  • Kok Lay Teo

    (Sunway University
    Tianjin University of Finance and Economics)

  • Xian-Jun Long

    (Chongqing Technology and Business University)

Abstract

This paper deals with robust $$\varepsilon $$ ε -quasi Pareto efficient solutions of an uncertain semi-infinite multiobjective optimization problem. By using robust optimization and a modified $$\varepsilon $$ ε -constraint scalarization methodology, we first present the relationship between robust $$\varepsilon $$ ε -quasi solutions of the uncertain optimization problem and that of its corresponding scalar optimization problem. Then, we obtain necessary optimality conditions for robust $$\varepsilon $$ ε -quasi Pareto efficient solutions of the uncertain optimization problem in terms of a new robust-type subdifferential constraint qualification. We also deduce sufficient optimality conditions for robust $$\varepsilon $$ ε -quasi Pareto efficient solutions of the uncertain optimization problem under assumptions of generalized convexity. Besides, we introduce a Mixed-type robust $$\varepsilon $$ ε -multiobjective dual problem (including Wolfe type and Mond-Weir type dual problems as special cases) of the uncertain optimization problem, and explore robust $$\varepsilon $$ ε -quasi weak, $$\varepsilon $$ ε -quasi strong, and $$\varepsilon $$ ε -quasi converse duality properties. Furthermore, we introduce an $$\varepsilon $$ ε -quasi saddle point for the uncertain optimization problem and investigate the relationships between the $$\varepsilon $$ ε -quasi saddle point and the robust $$\varepsilon $$ ε -quasi Pareto efficient solution for the uncertain optimization problem.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joptap:v:191:y:2021:i:1:d:10.1007_s10957-021-01938-4
    DOI: 10.1007/s10957-021-01938-4
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    References listed on IDEAS

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    1. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "Characterizations for Optimality Conditions of General Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 835-856, June.
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    5. 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.
    6. T. Son & D. Kim, 2013. "ε-Mixed type duality for nonconvex multiobjective programs with an infinite number of constraints," Journal of Global Optimization, Springer, vol. 57(2), pages 447-465, October.
    7. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 466-493, February.
    8. 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.
    9. Xiangkai Sun & Kok Lay Teo & Liping Tang, 2019. "Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 984-1000, September.
    10. Jonas Ide & Anita Schöbel, 2016. "Robustness for uncertain multi-objective optimization: a survey and analysis of different concepts," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 235-271, January.
    11. Zai-Yun Peng & Jian-Wen Peng & Xian-Jun Long & Jen-Chih Yao, 2018. "On the stability of solutions for semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 70(1), pages 55-69, January.
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    Cited by:

    1. 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.

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