A class of nonlinear optimisation and applications

2012/03/11 by Jiakun Liu, Liu, Jiakun
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.1203.2351

openalex publication_date 2012/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. We also present some interesting applications in optimal transportation and geometric optics problems.

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions

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