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Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications

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  • Thinh, Vo Duc
  • Chuong, Thai Doan
  • Le Hoang Anh, Nguyen

Abstract

In the paper, we start by establishing first and second-ordered analysis for a convex inequality system that contains uncertainty data, including calculating normal and tangent cones, second-ordered tangent sets for the solution set to this system, and first and second-ordered epi-subderivatives for the indicator function of its solution set. Then, we provide second-ordered necessary and sufficient optimality conditions for strict solutions of convex robust optimization problems. Moreover, an associated algorithm converging quickly to a solution for the class of quadratic robust optimization problems is proposed. The theoretical results are newly obtained under weak qualification conditions, and numerical examples show the advantage of the given method.

Suggested Citation

  • Thinh, Vo Duc & Chuong, Thai Doan & Le Hoang Anh, Nguyen, 2023. "Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications," Applied Mathematics and Computation, Elsevier, vol. 455(C).
    • Handle: RePEc:eee:apmaco:v:455:y:2023:i:c:s0096300323002837
    DOI: 10.1016/j.amc.2023.128114
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    References listed on IDEAS

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    1. V. D. Thinh & T. D. Chuong & N. L. H. Anh, 2023. "Second order analysis for robust inclusion systems and applications," Journal of Global Optimization, Springer, vol. 85(1), pages 81-110, January.
    2. Chen Ling & Qin Ni & Liqun Qi & Soon-Yi Wu, 2010. "A new smoothing Newton-type algorithm for semi-infinite programming," Journal of Global Optimization, Springer, vol. 47(1), pages 133-159, May.
    3. Tuan, Nguyen Dinh, 2015. "First and second-order optimality conditions for nonsmooth vector optimization using set-valued directional derivatives," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 300-317.
    4. C. Ling & L. Q. Qi & G. L. Zhou & S. Y. Wu, 2006. "Global Convergence of a Robust Smoothing SQP Method for Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 129(1), pages 147-164, April.
    5. Dong-Hui Li & Liqun Qi & Judy Tam & Soon-Yi Wu, 2004. "A Smoothing Newton Method for Semi-Infinite Programming," Journal of Global Optimization, Springer, vol. 30(2), pages 169-194, November.
    6. Chuong, T.D. & Jeyakumar, V., 2017. "Convergent hierarchy of SDP relaxations for a class of semi-infinite convex polynomial programs and applications," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 381-399.
    7. Jiachen Ju & Qian Liu, 2020. "Convergence properties of a class of exact penalty methods for semi-infinite optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 383-403, June.
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