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Characterization of unique solvability of absolute value equations: an overview, extensions, and future directions

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This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompasses known results as well as novel characterizations proposed in this study.

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Acknowledgements

S. Kumar was supported by the Ministry of Education, Government of India, through Graduate Aptitude Test in Engineering (GATE) fellowship registration No. MA19S43033021. M. Hladík and Hossein Moosaei were supported by the Czech Science Foundation Grant P403-22-11117 S.

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Authors and Affiliations

  1. Department of Mathematics, PDPM-Indian Institute of Information Technology, Design and Manufacturing Jabalpur, Jabalpur, M.P., India

    Shubham Kumar

  2. Department of Mathematics, Faculty of Natural Sciences, PDPM-Indian Institute of Information Technology, Design and Manufacturing Jabalpur, Jabalpur, M.P., India

    Deepmala

  3. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranske nam. 25, 118 00, Prague, Czech Republic

    Milan Hladík

  4. Department of Informatics, Faculty of Science, Jan Evangelista Purkyně University, Ústí nad Labem, Czech Republic

    Hossein Moosaei

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Kumar, S., Deepmala, Hladík, M. et al. Characterization of unique solvability of absolute value equations: an overview, extensions, and future directions. Optim Lett 18, 889–907 (2024). https://doi.org/10.1007/s11590-024-02094-0

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