## linear programming optimization equality constraints

### anu vru (view profile)

on 14 Feb 2018
Latest activity Edited by Matt J

on 14 Feb 2018

### Matt J (view profile)

hello, i am trying to do linear programming. and i am trying to find the minimum of my objective function.
i have attached the code. and my problem statement is also attached. i keep getting error for my equality constraints i tried every possible way known to me to solve. still couldn't fix it if anyone could suggest a way, it would be really helpful thank you

anu vru

### anu vru (view profile)

on 14 Feb 2018
Well, I need the X values which will make my pv+pw-L=0...
I need the X values for Pv and PW... And I am pretty sure my code doesn't consider them as constants
Matt J

### Matt J (view profile)

on 14 Feb 2018
Well, I need the X values which will make my pv+pw-L=0...
There are no X values appearing anymore in the expression pv+pw-L. Are we still talking about pv*x(1)+pw*x(2)-L=0?
Similarly, is the objective still f(x) = pv*x(1)+pw*x(2) ?
anu vru

### anu vru (view profile)

on 14 Feb 2018
Yes....I need the x

on 14 Feb 2018
Edited by Matt J

### Matt J (view profile)

on 14 Feb 2018

for that that L I need values for x(1) and x(2)...such that pv*x(1)+pw*x(2)-L=0 or atleast close to Zero
The above is a a version of what you said here with corrections added by me based on your later comments.
If the whole point is really to minimize |pv*x(1)+pw*x(2)-L| subject to bounds on x, then you should really be using lsqlin:
N=length(pv);
clear x
for i=N:-1:1
f=[pv(i) pw(i)];
[x{i} fval{i}]=lsqlin(f,l(i),[],[],[],[], [0.5,0.5],[2.5,2]);
end

anu vru

### anu vru (view profile)

on 14 Feb 2018
yes its working now
also is a way i could get all the possible solutions?? for example
pv=1;pw=2 and L=4
therefore my x values can be x=[0 2] or x=[2 1] and more non integer answers. is there a possibility i can get all those values??
i have further analysis to do on it.
anu vru

### anu vru (view profile)

on 14 Feb 2018
"the trust region reflective algorithm requires at least as many equations as variables" It is showing this warning... Also how is using lsqlin better than linprog?
Matt J

### Matt J (view profile)

on 14 Feb 2018
yes its working now
The set of all possible solutions will typically be an infinite set of points satisfying the inequalities,
L-optimalValue <= pv*x1+pw*x2 <= L+optimalValue
lbv<= x(1) <=ubv
lbw<= x(2) <=ubw
You can find the vertices of this region using this package.