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Second order variational analysis of disjunctive constraint sets and its applications to optimization problems

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Abstract

In this paper, we examine the properly twice epi-differentiability and compute the second order epi-subderivative of the indicator function to a class of sets including the finite union of parabolically derivable and parabolically regular sets. In this way, we provide no-gap second order optimality conditions for a disjunctive constrained problem. Moreover, we derive applications of our results to some types of disjunctive programs.

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Acknowledgements

The authors would like to thank the editor and referees for valuable comments and suggestions. V. D. Thinh: Research of this author was supported by the Domestic Master/PhD Scholarship Programme of Vingroup Innovation Foundation under Grant VINIF.2019.TS.61.

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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. Department of Mathematics Teacher Education, Dong Thap University, Cao Lãnh, Dong Thap Province, Vietnam

    V. D. Thinh

  4. School of Information Technology, Deakin University, Burwood VIC, Australia

    T. D. Chuong

  5. Department of Mathematics and Applications, Saigon University, 273 An Duong Vuong Street, Ward 3, District 5, 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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Thinh, V.D., Chuong, T.D. & Anh, N.L.H. Second order variational analysis of disjunctive constraint sets and its applications to optimization problems. Optim Lett 15, 2201–2224 (2021). https://doi.org/10.1007/s11590-020-01681-1

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  • DOI: https://doi.org/10.1007/s11590-020-01681-1

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