A class of nonlinear optimization problems with potentials

Details A class of nonlinear optimization problems with potentials A class of nonlinear optimization problems with potentials

2012-03-11

arxiv.org/abs/1203.2351v1

Mathematics

Analysis of PDEs

Scientific paper

In this paper, we introduce a class of nonlinear optimization problems. Under
mild assumptions, we obtain the existence of potential functions and show that
the potential function is a generalized 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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