On non-linear optimization with a perturbed objective function
Optimization and Control
2021-06-29 v1
Abstract
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise differentiation, and an approximate Fermat Lemma and Implicit Function Theorem. The tools are the external numbers of Nonstandard Analysis, which are models of Sorites imprecisions.
Cite
@article{arxiv.2106.14569,
title = {On non-linear optimization with a perturbed objective function},
author = {Nam Van Tran and Imme van den Berg},
journal= {arXiv preprint arXiv:2106.14569},
year = {2021}
}
Comments
20 pages