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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.17596 |
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Table of Contents:
- We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones; they can be optimised via exact line search along admissible directions, and the iterates then inherit a bidimensional optimality property. We study the minimisation of such relaxed maps via coordinate descents with gradient-based rules, placing a special emphasis on coordinate directions verifying a maximum-alignment property in the reproducing kernel Hilbert spaces related to the underlying positive-semidefinite matrices. In this setting, we illustrate that accounting for the optimal rescaling of the iterates can in certain situations substantially accelerate the unconstrained minimisation of convex quadratic maps.