Nonconvex optimization via analysis in image space

The solution of a particular nonconvex program is usually very dependent on the structure of the problem. In this paper the authors identify classes of nonconvex problems involving sums or products of ratios of linear terms which may be treated by analysis in a transformed space. In each class, the image space is defined by a mapping which associates a new variable with each original ratio of linear terms. In the image space, optimization is easy in certain directions, and the overall solution may be realized by sequentially optimizing in these directions.