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• W2108140204 abstract "In this paper, we use the concept of barrier-based smoothing approximations introduced by Chua and Li [SIAM J. Optim., 23 (2013), pp. 745--769] to extend the smoothing Newton continuation algorithm of Hayashi, Yamashita, and Fukushima [SIAM J. Optim., 15 (2005), pp. 593--615] to variational inequalities over general closed convex sets $X$. We prove that when the underlying barrier has a gradient map that is definable in some o-minimal structure, the iterates generated converge superlinearly to a solution of the variational inequality. We further prove that if $X$ is proper and definable in the o-minimal structure $mathbb{R}_{mathrm{an}}^{mathbb{R}_{mathrm{alg}}}$, then the gradient map of its universal barrier is definable in the o-minimal expansion $mathbb{R}_{mathrm{an}, exp}$. Finally, we consider the application of the algorithm to complementarity problems over epigraphs of matrix operator norm and nuclear norm and present preliminary numerical results." @default.
• W2108140204 created "2016-06-24" @default.
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• W2108140204 date "2015-01-01" @default.
• W2108140204 modified "2023-09-27" @default.
• W2108140204 title "A Superlinearly Convergent Smoothing Newton Continuation Algorithm for Variational Inequalities over Definable Sets" @default.
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• W2108140204 doi "https://doi.org/10.1137/140957615" @default.
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