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Given the quadratic programming problem \begin{align*} min \quad 0.5(x_1-a)^2+0.5(x_2-b)^2+0.5(x_3-c)^2\\ s.t \quad 4x_1+5x_2=20\\ 8x_1+3x_2+12x_3=24 \end{align*} Use the method of projection to obtain analytically the optimal solution in terms of $a,b,$ and $c$.

Can anyone help me how to figure this out? Any help or even a hint is highly appreciated. Thanks.

Andre Jackson
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  • Have a look at https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&ved=2ahUKEwjisMCg6bHiAhUix4UKHfyaBJUQFjAEegQICRAC&url=http%3A%2F%2Fusers.jyu.fi%2F~jhaka%2Fopt%2FTIES483_constrained_direct1.pdf&usg=AOvVaw2Y2rIKFelH4rK10STrrWSB – Claude Leibovici May 23 '19 at 14:09
  • WA says this here $$\left{\frac{1}{836} \left(193 a^2+360 a b+210 a c-1580 a+274 b^2-168 b c-2080 b+369 c^2+180 c+4100\right),\left{\text{x1}\to \frac{5}{418} (45 a-36 b-21 c+158),\text{x2}\to \frac{1}{5} \left(20-\frac{10}{209} (45 a-36 b-21 c+158)\right),\text{x3}\to \frac{1}{12} \left(-\frac{3}{5} \left(20-\frac{10}{209} (45 a-36 b-21 c+158)\right)-\frac{20}{209} (45 a-36 b-21 c+158)+20\right)\right}\right}$$ – Dr. Sonnhard Graubner May 23 '19 at 15:25

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