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- W4313198125 abstract "We consider the problem of finding the best approximation point from a polyhedral set, and its applications, in particular to solving large-scale linear programs. The classical projection problem has many various and many applications. We study a regularized nonsmooth Newton type solution method where the Jacobian is singular; and we compare the computational performance to that of the classical projection method of Halperin-Lions-Wittmann-Bauschke (HLWB). We observe empirically that the regularized nonsmooth method significantly outperforms the HLWB method. However, the HLWB has a convergence guarantee while the nonsmooth method is not monotonic and does not guarantee convergence due in part to singularity of the generalized Jacobian. Our application to solving large-scale linear programs uses a parametrized projection problem. This leads to a emph{stepping stone external path following} algorithm. Other applications are finding triangles from branch and bound methods, and generalized constrained linear least squares. We include scaling methods that improve the efficiency and robustness." @default.
- W4313198125 created "2023-01-06" @default.
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- W4313198125 date "2022-12-26" @default.
- W4313198125 modified "2023-09-27" @default.
- W4313198125 title "Regularized Nonsmooth Newton Algorithms for Best Approximation" @default.
- W4313198125 doi "https://doi.org/10.48550/arxiv.2212.13182" @default.
- W4313198125 hasPublicationYear "2022" @default.
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