I am comparing LP's and SDP's and have come across a lot of papers where they show all of the differences, but I am trying to put an lp is sdp form. The reason being I have solved an advanced sdp using an online solver and can solve basic/advanced lps on my pc, but I now want to take a lp and show that it can be solved using sdp (as lp is just a special case of sdp).(adsbygoogle = window.adsbygoogle || []).push({});

Start with the simple LP: min: 3x + 4y ;

Constraints: 3x - 4y <= 12;

x + 2y >= 4;

y >= 0;

x >= 1

How would this look as an sdp in the form:

min 3x + 4y

x=f1x + f2y -f0

x>=0

f0, f1, f2 = ?,?,?

---

Also how would I reverse engineer an sdp into an lp:

Example:

min 10x1+20x2

st X=F1x1+F2x2-F0

X >= 0

F0=[1 0 0 0

0 2 0 0

0 0 3 0

0 0 0 4]

F1=[1 0 0 0

0 1 0 0

0 0 0 0

0 0 0 0]

F2=[0 0 0 0

0 1 0 0

0 0 5 2

0 0 2 6]

What would my constraints for the lp be? (I know there may not be feasible solution for this sdp in lp form).

Thanks in advance, Oli

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# Writing a Linear program as a semi definite program

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