Numerical Optimization ( norm minim)

by sbashrawi
Tags: minim, norm, numerical, optimization
 HW Helper P: 3,307 consider the set $\left\{ x \in \mathbb{R}^n : ||x||^2 = c\}$ for some constant c, geometrically what does it represent? now consider the half space, the boundary of which is a plane. how does the plane intersect the above set, in particular for the minimum value of c. This should lead to a simple solution
 P: 55 Numerical Optimization ( norm minim) Here is my work: f(x) = ||x|| ^2 subjeted to c(x) = a^{T} x +$$\alpha$$$$\geq$$0 so L ( x,$$\lambda$$) = f(x) - $$\lambda$$ c(x) gradiant L(x,$$\lambda$$) = 2x - $$\lambda$$ grad(c(x)) = 0 grad c(x)= a so 2x - $$\lambda$$a = 0 this gives that x = $$\frac{}{}[1/2]\lambda$$a and c(x) = 0 gives : $$\lambda$$ = -2 $$\alpha$$$$/ ||a||^2 imlpies x = - \alpha$$ a / ||a||^2