Methods and Applications of Analysis
Volume 28 (2021)
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
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