linear programming optimization equality constraints

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

[Matt J]

The problem in your problemstatement.txt is pretty absurd (so I'm wondering if there is a mistake). The objective function is constant over the constrained region, so all feasible points (if any exist) are optimal.

[anu vru]

how exactly is it absurd?? i have a function to minimize my coefficients change over a period of time.

[anu vru]

"Are you solving a separate sub-problem for every pv(i), pw(i), l(i) or something else?"

Yes

I need X(i) for every value of PV(I) PW(I) and l(I)

For the second part... I need to do (PV+pw-L) this is my objective...but my L is constant..I cannot vary that....for that that L I need values for Pv and PW...such that pv+pw-L=0 or atleast close to Zero

[Matt J]

In your problem statement document, pv, pw, and L appear to be scalars, yet in your code they are vectors. You need to help us reconcile that. Are you solving a separate sub-problem for every pv(i), pw(i), l(i) or something else?

In any case, the problem as written is absurd because as I said, all choices of x(1) and x(2) are equally optimal. Your constraint

   (pv*x(1)+pw*x(2))=L

assures that the objective function

   f(x)=(pv*x(1)+ pw*x(2))

is a constant f(x)=L over all feasible x.

[Matt J]

For the second part... I need to do (PV+pw-L) this is my objective...

What happened to the x(i)'s?

but my L is constant..I cannot vary that....for that that L I need values for Pv and PW...such that pv+pw-L=0 or atleast close to Zero

You need Pv and PW? But in your code, they are given constants!

[anu vru]

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]

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]

Yes....I need the x

Answer 1

[Matt J]

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]

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]

"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]

yes its working now

If so, please Accept-click the answer to certify that the question has been addressed.

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.