An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence
Optimization and Control
2023-05-01 v1
Abstract
Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In this paper we combine a classical adaptive discretization method developed by Blankenship and Falk and techniques regarding a semi-infinite optimization problem as a bi-level optimization problem. We develop a new adaptive discretization method which combines the advantages of both techniques and exhibits a quadratic rate of convergence. We further show that a limit of the iterates is a stationary point, if the iterates are stationary points of the approximate problems.
Cite
@article{arxiv.1910.13798,
title = {An adaptive discretization method solving semi-infinite optimization problems with quadratic rate of convergence},
author = {Tobias Seidel and Karl-Heinz Küfer},
journal= {arXiv preprint arXiv:1910.13798},
year = {2023}
}