When using Fmincon, how to avoid using "max", "if-else-end" in the constraints?

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Tao
Tao 2016-1-28
评论： Tao 2016-1-28
I have some functions which will be called by the constraints, for example:
mx = 1.4 - 1.1*10^(-4)*Jz - 0.2*10^(-8)*Jz^2;
It could be that Jz is quite big and mx will be smaller than 0. Is that OK to modify this function like below ?
mx = max(1.4 - 1.1*10^(-4)*Jz - 0.2*10^(-8)*Jz^2, 0);
Will Fmincon like this? If not, how to avoid it? Thank you!

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回答（1 个）

Walter Roberson
Walter Roberson 2016-1-28
If Jz is one of the inputs, then split the task into three pieces,
Jz < -27500-2500*sqrt(233)
Jz > -27500+2500*sqrt(233)
-27500-2500*sqrt(233) <= Jz <= -27500+2500*sqrt(233)
In the first two cases, the constraint function should hard-code mz as 0; in the third case, use your current calculation. Run all three cases, and take the best of the results.
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Walter Roberson
Walter Roberson 2016-1-28
I was asking if Jz is one of the variables being optimized.
Is it possible to place a linear constraint on the variables being optimized, so that Jz will not exceed the range I indicated?
Yes, I did mean run the three cases independently using fmincon()
Using min() or max() or if/else in a nonlinear constraint is not always a problem. However, when the boundary cannot be expressed as a linear combination of the variables being optimized, you run the risk that you are breaking up the input space into non-continguous regions, and if that happens then fmincon's algorithms will fail. If the nonlinear constraints are acting to create a dividing hyperplane that is just difficult to express linearly, then you are probably okay.
Tao
Tao 2016-1-28
It looks like this:
Unknown variables: x(1), x(2),..., x(10), x(11)
Objective function: -x(10)
low bounds for x: lb = [0;0;0;0;0;0;0;0;(-1);(0);(-1)];
high bounds for x: ub = [1;1;1;1;1;1;1;1;( 1);(1);( 1)];
Constraints: Jz = Function_1(x);
Fxy = mx(Jz);
c = Function_2 (Fxy);
ceq = Function_3 (x);

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