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arXiv · 1203.2351

A class of nonlinear optimisation and applications

Jiakun Liu
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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-Amp\`ere type equation. We also present some interesting applications in optimal transportation and geometric optics problems.

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Jiakun Liu. 2012-03-11. A class of nonlinear optimisation and applications. https://arxiv.org/abs/1203.2351

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