Methods and Applications of Analysis

Volume 28 (2021)

Number 1

Special Issue for the 60th Birthday of John Urbas: Part II

Guest Editors: Neil Trudinger and Xu-Jia Wang

A class of nonlinear optimisation and applications

Pages: 31 – 52

DOI:  https://dx.doi.org/10.4310/MAA.2021.v28.n1.a3

Author

Jiakun Liu (School of Mathematics and Applied Statistics, University of Wollongong, NSW, Australia)

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–Ampère type equation.

Keywords

nonlinear optimisation, potential function, Monge–Ampère equation

2010 Mathematics Subject Classification

28C99, 35B45, 35J60, 49Q20

This work is supported by the Australian Research Council, DP170100929 and DP200101084.

Received 3 April 2020

Accepted 15 July 2020

Published 1 December 2021