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arXiv · 2404.15571

A note on the generalised Hessian of the least squares associated with systems of linear inequalities

M. V. Dolgopolik
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Abstract

The goal of this note is to point out an erroneous formula for the generalised Hessian of the least squares associated with a system of linear inequalities, that was given in the paper "A finite Newton method for classification" by O.L. Mangasarian (Optim. Methods Softw. 17: 913--929, 2002) and reproduced multiple times in other publications. We also provide sufficient contiditions for the validity of Mangasarian's formula and show that Slater's condition guarantees that some particular elements from the set defined by Mangasarian belong to the generalised Hessian of the corresponding function.

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M. V. Dolgopolik. 2024-04-24. A note on the generalised Hessian of the least squares associated with systems of linear inequalities. https://doi.org/10.1080/10556788.2024.2372660

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