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arXiv · 2208.09073

Linear optimization on varieties and Chern-Mather classes

Laurentiu G. Maxim·Jose Israel Rodriguez·Botong Wang·Lei Wu
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Abstract

The linear optimization degree gives an algebraic measure of complexity of optimizing a linear objective function over an algebraic model. Geometrically, it can be interpreted as the degree of a projection map on the {affine} conormal variety. Fixing an affine variety, our first result shows that the geometry of {this} conormal variety, expressed in terms of bidegrees, completely determines the Chern-Mather classes of the given variety. We also show that these bidegrees coincide with the linear optimization degrees of generic affine sections.

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Laurentiu G. Maxim, Jose Israel Rodriguez, Botong Wang, Lei Wu. 2022-08-18. Linear optimization on varieties and Chern-Mather classes. https://arxiv.org/abs/2208.09073

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