A simple-shaped non-contiguous area cartogram is one of the visualization tools of spatial data; regions are represented by simple shapes, such as circles or rectangles, and their sizes are proportional to statistical data values. The construction of simple-shaped non-contiguous area cartograms is to place the given simple-shapes to represent the geographic configuration and contiguity of regions and to avoid overlaps of shapes. In this study, a new approach for their construction is proposed. The proposed approach formulates the construction as non-linear optimization problems with inequality constraints. The formulation by proposed approach is tested through the construction of rectangular cartograms, one type of non-contiguous cartograms, using the world population data. The result confirms that the proposed approach is applicable to the construction of simple-shaped non-contiguous area cartograms.