How many Minimum Non Linear equations required to solve N variables in optimization problem?

I am using Genetic Algorithm to optimize the decision variables x(1),x(2),....x(N).

And I have less than N equations obtained from constraint function, With only one Objective.

Do we exactly need N non-linear equations? Or is it ok if we have less than N equations?

Answer 1

[Birdman]

Imagine that N=3;

A=[1 1 4;2 4 5];b=[2;1];
fun=@(x) x(1).^2+2*x(2)-x(3).^3;
y=ga(fun,3,A,b)

As you can see, there is one objective function, with two constraints and three variables. It gives a result. Hope this helps.

[Dhanu Naik]

Thank you for your time,

But I am solving a problem to obtain global minima and my inputs to GA are like this

[X,f]=ga(fcn,N,[],[],[],[],[],[],consfcn, options)

Where N is Large say 32 and Constraints function can form less than N non-linear equations say 25.

But I have only one objective function. Can GA provide optimum values of X and minimum value of objective function?

[Birdman]

Yes, it can but it will just take more time than usual. For instance for N=32, when I solve a problem for ga, the elapsed time is

>>  Elapsed time is 73.111 seconds.

[Dhanu Naik]

Thank you, I hope this will help me.

Answer 2

[Torsten]

Any number of constraint functions is ok.

Best wishes

Torsten.