Multi functions multi variables optimization

Hello, I am looking for a better optimization method or algorithm.

Here, I have some variables and some functions.

For example,

I have 5 variables: a, b, c, d, e.

And 4 functions(maybe not 4): 0<F(a,b,c,d,e)<=0.01, 0<G(a,b,c,d,e)<=0.01, 0.9<=H(a,b,c,d,e)<=0.95, I(a,b,c,d,e)=sqrt(1-H(a,b,c,d,e)^2).

BTW, the functions are nonlinear functions, it is complicate and contains cos(),sin().etc.

The variables have constraints:

1<a<2; 2<b<3; 3<c<4; 4<d<5; 5<e<6;

I would like to find the solution under these variable constraints.

I used fsolve before, But I think they are not suitable in this situation.

I am not familiar with optimization algorithm, could any one help me give me some suggestions to address this problem?

I am appreciate if you give me an example to solve those equations. Thank you very much!

Answer 1

[Torsten]

Use fmincon.

Define the constraints

1<a<2; 2<b<3; 3<c<4; 4<d<5; 5<e<6

in lb and ub,

define the constraints

0<F(a,b,c,d,e)<=0.01, 0<G(a,b,c,d,e)<=0.01, 0.9<=H(a,b,c,d,e)<=0.95, I(a,b,c,d,e)=sqrt(1-H(a,b,c,d,e)^2)

in the function nonlcon for nonlinear constraints in the array c.

Then simply define the objective function as "0" since you don't want to minimize anything, but you only want to find a feasible point a,b,c,d,e for your problem.

[Alan Weiss]

Torsten is, as usual, spot on. I just want to add that this topic is addressed in the documentation:

Nonlinear Systems with Constraints

and

Nonlinear System of Equations with Constraints, Problem-Based.

Alan Weiss

MATLAB mathematical toolbox documentation