A class of nonlinear optimisation and applications
Analysis of PDEs
2019-09-13 v2 Optimization and Control
Abstract
In this paper, we introduce a class of nonlinear optimisation problems. Under mild assumptions, we obtain the existence of potential functions and show that the potential function is a generalised solution of a Monge-Amp\`ere type equation. We also present some interesting applications in optimal transportation and geometric optics problems.
Cite
@article{arxiv.1203.2351,
title = {A class of nonlinear optimisation and applications},
author = {Jiakun Liu},
journal= {arXiv preprint arXiv:1203.2351},
year = {2019}
}