Light reflection is nonlinear optimization

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

paper · pdf · doi:10.48550/arxiv.1203.2350

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

Abstract

In this paper, we show that the near field reflector problem is a nonlinear optimization problem. From the corresponding functional and constraint function, we derive the Monge-Ampère type equation for such a problem.

Citations

• Polar factorization and monotone rearrangement of vector‐valued functions

Related

• The reflector problem and the inverse square law
• Weak solutions to the near-field reflector problem with spatial restrictions approached with generalized reflectors constructed from ellipsoids
• Optimal Transportation for the Far-field Reflector Problem
• Pointwise estimates and regularity in geometric optics and other Generated Jacobian Equations
• A class of nonlinear optimisation and applications