Support quadric method in non-imaging optics problems that can be reformulated as a mass transfer problem

The article deals with problems of generating desired illumination patterns, formulated in a special way. More precisely, we consider problems that can be reformulated as a Monge-Kantorovich mass transfer problem with some cost function. For all problems of this type, we uniformly formulate the support quadric method and show that it coincides with the gradient method for finding the maximum of a certain concave function.