subject- Optimization

3. Consider two points, v1,v2Rn. In this exercise you will show that there exists a vector cRn and a scalar dR such that {x:xv12xv22}={x:cxd}. 1 - Two dimensions: consider the above problem in two dimensions, where v1=(1,0), and v2=(1,0). Draw the set of points that are closer to v1 than v2, by shading the plane. This should be a half-space! - For the above example, find the two-dimensional vector c=(c1,c2) and the scalar d that describes the shaded region from the above. So in other words, the shaded region you drew must correspond do: {(x1,x2):c1x1+c2x2d}. - Finally, generalize the above. For general points v1,v2Rn, find a vector cRn and a scalar dR such that {x:xv12xv22}={x:cxd}. Thus, you are showing that the set of points in Rn that are closer to point v1 than to point v2, form a half-space