Consider the placement of three circles of different diameter in a box enclosure of minimum perimeter. As shown in Figure 6.7, this leads to the following nonconvex, constrained NLP:

where Ri is the radius of circle i, (xi,yi) represents the center of circle i, and a and b are the horizontal and vertical sides of the box, respectively.

Let Ri = 1+i/10. Apply an SQP solver to this algorithm with starting points x0 i = i, y0 i = i, a0 = 6, and b0 = 6.

Repeat this study using an interior point NLP solver