jelentetvq

2022-02-01

An inequality constraint problem
$min\frac{1}{2}{\left({x}_{1}-1\right)}^{2}+\frac{1}{2}{\left({x}_{2}-2\right)}^{2}$
s.t.

Flickkorbma

Expert

Write , then you have to find a minumum of
$f\left(t\right)={t}^{2}+{\left(t-2\right)}^{2}=2{t}^{2}-4t+4$
where $t\le \frac{1}{2}$. Since it global minimum is at $t=1$ we see that it is decreasing on $\left(-\mathrm{\infty },1\right)$, so
$f\left(t\right)\ge f\left(\frac{1}{2}\right)=...$

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