On Second-Order Cone Functions

Figure 4

The geometry of the second-order cone function , with and , is defined in Example 3. The function can also be written as , where . The maximum of is at , and the maximum value is . The orthogonal projection of onto the column space of is . The distance from to is . One contour of is shown. The image of this contour is a circle of points in that are equidistant from .