Solving equation problem with constrains using the Optimization Toolbox

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MENGZE WU
MENGZE WU 2021-11-12
评论： Matt J 2021-11-12
I have a problem with handful of variables and constrains, it look a lot like this one:
Set Up a Linear Program, Problem-Based - MATLAB & Simulink (mathworks.com)
However, instead of finding the minimum cost like the problem above, I already have a target cost, but find the variables that fits this target cost. So I look at the equation problems:
Create equation problem - MATLAB eqnproblem (mathworks.com)
But it seems that the equation problem wouldn't allow me to add constrains, what should I do?

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Matt J
Matt J 2021-11-12
编辑：Matt J 2021-11-12
Ran in:
Use your first approach except specify a least squares objective, like below.
x=optimvar('x','lower',0);
y=optimvar('y','lower',0);
target=10; %target cost
con(1)=x>=y;
con(2)=x+y>=1;
solve( optimproblem('Objective', (x+2*y-target).^2,'Constraints',con) )
Solving problem using lsqlin. Minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.
ans = struct with fields:
x: 3.8238 y: 3.0881
Be mindful, however, that the solution will probably be non-unique. For example, another solution to the example problem above is x=10, y=0.
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Walter Roberson
Walter Roberson 2021-11-12
If the set of solutions is all points on a particular line or particular plane, then you cannot return them all -- not unless you want to iterate over each distinguishable floating point number in the range.
That is why I was suggesting that the system needed to be integer constrained variables: for those it is possible to list all of the solutions (but it might need a lot of memory if the set of points is large enough.)
Matt J
Matt J 2021-11-12
If the set of solutions is all points on a particular line or particular plane, then you cannot return them all
No, you can't, but it will be a convex polyhedral region and, if bounded, you can use its vertices both to plot the region and to sample an arbitrary number of points from its interior.

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