Moslem Zamani and Milan Hladík. A new concave minimization algorithm for the absolute value equation solution. Optim. Lett., 15(6):2241–2254, September 2021.
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In this paper, we study the absolute value equation (AVE) $Ax-b=|x|$. One effective approach to handle AVE is by using concave minimization methods. We propose a new method based on concave minimization methods. We establish its finite convergence under mild conditions. We also study some classes of AVEs which are polynomial time solvable.
@article{ZamHla2021a,
author = "Moslem Zamani and Milan Hlad\'{\i}k",
title = "A new concave minimization algorithm for the absolute value equation solution",
journal = "Optim. Lett.",
fjournal = "Optimization Letters",
volume = "15",
number = "6",
month = "September",
pages = "2241-2254",
year = "2021",
doi = "10.1007/s11590-020-01691-z",
issn = "1862-4480",
url = "https://link.springer.com/article/10.1007/s11590-020-01691-z",
bib2html_dl_html = "https://doi.org/10.1007/s11590-020-01691-z",
bib2html_dl_pdf = "https://rdcu.be/cv0rx",
abstract = "In this paper, we study the absolute value equation (AVE) $Ax-b=|x|$. One effective approach to handle AVE is by using concave minimization methods. We propose a new method based on concave minimization methods. We establish its finite convergence under mild conditions. We also study some classes of AVEs which are polynomial time solvable.",
keywords = "Absolute value equation; Concave minimization algorithms; Linear complementarity problem",
}
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