I am looking for code, that is inverse of optimization. Have variable combinations (and plot them) that gives response value in a boundary.

For example

Y=3a+2b+5c-6a^2+7b^2

...is model. I want to have a, b, c combinations values that result in Y within -2 & +2. In addition, the subset of a, b, c must be in a given boundary i.e. -3<a<2, 4<b<7, 9<c<18 etc.

[Walter Roberson]

Is the question to determine all such values? There would be an indefinite number of such values if you permit floating point.

[Biswanath Mahanty]

I understand, there is an infinite number of plausible solution. However, I need to draw a surface plot, with adequate combinations.

Answer 1

[Walter Roberson]

Y = 200;   %for example

N = 50;
av = linspace(-3,2,N);
bv = linspace(4,7,N);
cv = linspace(9,18,N);
[a,b,c] = ndgrid(av,bv,cv);
dy = 3*a + 2*b + 5*c - 6*a.^2 + 7*b.^2 - Y;
mask = dy > -2 & dy < 2;
scatter3(a(mask), b(mask), c(mask))

[Biswanath Mahanty]

Thank you Walter Roberson. Your directives are great to start. However, when we are imposing mask onto a,b,c grids its a vector, not matrix. The results are fine with 3D scatter plot. But generating surface is not possible unless the a(mask), b(mask), c(mask) are reshaped into matrix.

[Walter Roberson]

You should not generate a surface plot for this: because you want Y within -2 & +2, you are defining a thickness with potentially multiple points instead of a surface.

Answer 2

[Alan Weiss]

You might be able to formulate this as an optimization problem. Your decision variables are a, b, c. The objective (the thing to minimize) is the sum of the squares (or absolute values) of the infeasibilities: max(Y,2) - 2 and abs(min(-2,Y) + 2).

To use Optimization Toolbox, formulate your problem in terms of one variable x = [a,b,c]. Then use the fmincon solver or the lsqnonlin solver. You can include bounds on the variables using the lb and ub arguments.

Alan Weiss

MATLAB mathematical toolbox documentation