I am not very sure of how the value x2* = -3/10 was derived. I tried differentiating wrt f([-1/2, alpha]) but I could not get the answer. Any help is appreciated in letting me better understand coordinate descent.
2026-03-27 01:42:40.1774575760
Coordinate Descent Method
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To find $x_2$, we minimize the function $$ g(\alpha) = f([-1/2,\alpha]) = 5\alpha^2 + 3\alpha + 5/4. $$ To optimize this function on one variable, we can simply differentiate to find the critical point. $$ g'(\alpha) = 10\alpha + 3 = 0 \implies \alpha = -\frac{3}{10} = -0.3. $$ Alternatively, you might remember from a precalculus class that the axis of a symmetry of the parabola $y = ax^2 + bx + c$ occurs at $x = -\frac{b}{2a}$.