Question

What is theoretical value for min(J(w)) for J(w) = (w1^2) + (w2^2) + 4w1 - 6w2 - 7? Please feek free to use matlab or any other software

Answer 1

obviously, it's not clear that what's your question in actual. if your question related to calculus { Maxima/ minima }

then, steps to find minimum value J(w) is given below :

J(w) = $w_1^2+w_2^2+4w_1-6w_2-7$

partially differentiating J(w) with respect to $w_1$, keeping $w_2$ as a constant term.

$\frac{\delta{j(w)}}{\delta{w_1}}=2w_1+0+4-0-0$

equate $\frac{\delta{j(w)}}{\delta{w_1}}$ with zero, we get, $w_1=-2$

Similarly, partially differentiating J(w) with respect to $w_2$ keeping $w_1$ as a constant term.

$\frac{\delta{j(w)}}{\delta{w_2}}=0+2w_2+0-6-0$

equate $\frac{\delta{j(w)}}{\delta{w_2}}$ with zero, we get, $w_2=3$

now, put value of $w_1$ and $w_2$ in J(w) you will get minimum value.

e.g., min{J(w)} = (-2)² + (3)² + 4(-2) - 6(3) - 7 = -20