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## Main Question or Discussion Point

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).

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

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