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 (Australian National University)

A class of nonlinear optimisation and applications

Pages: 31 – 52



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


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.


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