Light reflection is nonlinear optimization
Jiakun Liu
TL;DR
This paper demonstrates that the near field reflector problem can be formulated as a nonlinear optimization problem, deriving a Monge-Ampère type equation from the functional and constraints involved.
Contribution
It introduces a novel formulation of the near field reflector problem as a nonlinear optimization problem with a derived Monge-Ampère type equation.
Findings
The near field reflector problem is shown to be a nonlinear optimization problem.
A Monge-Ampère type equation is derived for this problem.
The formulation provides a new perspective for solving reflector design problems.
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-Amp\`ere type equation for such a problem.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Nonlinear Partial Differential Equations