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Second order analysis for robust inclusion systems and applications

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Abstract

In this paper, we study an uncertain inequality system, where the input data are uncertain and belong to prescribed uncertainty sets. Using the deterministic approach in robust optimization, we treat this uncertain system by examining the so-called robust system. This approach enables us to compute the second order tangent sets for the solution set of the robust system and then obtain the second order epi-subderivative for the indicator function of its solution set. In this way, we are able to calculate the graphical derivative for the normal cone mapping of solution set of the robust system under certain qualification conditions. As applications, we establish second order necessary and sufficient optimality conditions, and derive necessary and sufficient conditions for stability properties such as the isolated calmness of optimization problems involving uncertain constraints under weak qualification conditions.

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Acknowledgements

The authors would like to thank anonymous reviewers for the valuable comments and suggestions.

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Authors and Affiliations

  1. Department of Optimization and System Theory, University of Science, Ho Chi Minh City, Vietnam

    V. D. Thinh & N. L. H. Anh

  2. Vietnam National University, Ho Chi Minh City, Vietnam

    V. D. Thinh & N. L. H. Anh

  3. Dong Thap University, Cao Lanh City, Dong Thap Province, Vietnam

    V. D. Thinh

  4. Department of Mathematics and Applications, Saigon University, Ho Chi Minh City, Vietnam

    T. D. Chuong

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  1. V. D. Thinh
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  2. T. D. Chuong
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  3. N. L. H. Anh
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Correspondence to T. D. Chuong.

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V. D. Thinh: Research of this author was supported by the Domestic Master/PhD Scholarship Programme of Vingroup Innovation Foundation.

T. D. Chuong: Research of this author was supported by the National Foundation for Science and Technology Development of Vietnam (NAFOSTED) under grant number 101.01–2020.09.

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Thinh, V.D., Chuong, T.D. & Anh, N.L.H. Second order analysis for robust inclusion systems and applications. J Glob Optim 85, 81–110 (2023). https://doi.org/10.1007/s10898-022-01197-1

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  • DOI: https://doi.org/10.1007/s10898-022-01197-1

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