Shubham Kumar, Deepmala, Milan Hladík, and Hossein Moosaei. Characterization of unique solvability of absolute value equations: An overview, extensions, and future directions. Optim. Lett., 18(4):889–907, May 2024.
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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.
@article{KumDee2024,
author = "Shubham Kumar and Deepmala and Milan Hlad\'{\i}k and Hossein Moosaei",
title = "Characterization of unique solvability of absolute value equations: {An} overview, extensions, and future directions",
journal = "Optim. Lett.",
fjournal = "Optimization Letters",
volume = "18",
number = "4",
month = "May",
pages = "889-907",
year = "2024",
doi = "10.1007/s11590-024-02094-0",
issn = "1862-4480",
url = "https://link.springer.com/article/10.1007/s11590-024-02094-0",
bib2html_dl_html = "https://doi.org/10.1007/s11590-024-02094-0",
bib2html_dl_pdf = "https://rdcu.be/dEyqc",
abstract = "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.",
keywords = "Absolute value equations; Linear complementarity problem; Unique solution; Necessary and sufficient condition; Interval matrix; NP-hardness",
}
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