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Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization

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Abstract

We establish a generalized alternative theorem for nonquadratic nonconvex system by unifying S-lemma and convex Farkas lemma. As an application, we reveal hidden convexity of a new family of nonconvex optimization problems that combine generalized trust region subproblem with convex optimization.

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Acknowledgements

The authors are very grateful for the valuable comments from the associate editor and the two anonymous referees for their valuable comments, which have greatly improved the presentation of the paper. This research was supported by Beijing Natural Science Foundation Z180005, by National Natural Science Foundation of China under grants 11822103, 12101041, 12171021, by China Postdoctoral Science Foundation 2020M670490, 2020M680335, by the Fundamental Research Funds for the Central Universities FRF-TP-20-070A1.

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Authors and Affiliations

  1. School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Meijia Yang

  2. School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, People’s Republic of China

    Shu Wang

  3. LMIB of the Ministry of Education, School of Mathematical Sciences, Beihang University, Beijing, 100191, People’s Republic of China

    Yong Xia

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  1. Meijia Yang
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  2. Shu Wang
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  3. Yong Xia
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Correspondence to Yong Xia.

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Communicated by Marco Antonio López-Cerdá

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Yang, M., Wang, S. & Xia, Y. Toward Nonquadratic S-Lemma: New Theory and Application in Nonconvex Optimization. J Optim Theory Appl 194, 353–363 (2022). https://doi.org/10.1007/s10957-022-02031-0

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