Single and Multi-objective optimization

I have a three dimensional design space as shown in figure within which I need to perform single and multi-objective optimization. I cannot define the space with simple upper and lower bounds as such

x_lower = 0.0015;

X_upper = 1.2;

Y_lower = 0.0075;

Y_upper = 0.8;

Z_lower = 0.1;

Z_upper = 0.7;

Is it possible to define the space in a way such that only the space as shown in figure is explored ?

Answer 1

[Walter Roberson]

You can potentially use linear inequalities -- the A and b matrix.

linear inequalities are accepted by all forms of ga() and gamultiobj()

You can potentially use nonlinear inequalities and nonlinear equalities -- the nonlcon parameter,

Note: if you have integer constraints then you can use nonlinear inequalities, but nonlinear equalities. The ceq return value of the nonlcon function must be empty if you have integer constraints.

[neil vaz]

Well, I did use the convhull to find the boundries and then used unique to get the points that define the hull. Added them in the constraints A and the algorithim works. Thank you @Walter Roberson