On the Computation of Convergence Regions for Sequential Nonlinear Programming Problems

In this work, we formulate and solve the problem of finding the ball of maximum radius around a local minimum of a nonlinear optimization problem, which is invariant with respect to the gradient descent method. This problem arises in the context of solving sequences of nonlinear optimization problem...

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Bibliographic Details
Published in:Proceedings in applied mathematics and mechanics 2021-01, Vol.20 (1), p.n/a
Main Authors: Mykhailiuk, Ivan, Schäfer, Kai, Flaßkamp, Kathrin, Büskens, Christof
Format: Article
Language:English
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Summary:In this work, we formulate and solve the problem of finding the ball of maximum radius around a local minimum of a nonlinear optimization problem, which is invariant with respect to the gradient descent method. This problem arises in the context of solving sequences of nonlinear optimization problems, in which one usually strives to converge to qualitatively similar solutions. We illustrate our idea with an example of a nonlinear function of two variables.
ISSN:1617-7061
1617-7061
DOI:10.1002/pamm.202000281