Constrained optimization of a vector

Hi!

I am trying to optimize a vector. I want to find , where ()=0, and .

f_1 and f-2 are two procedural functions, stored in m-files (not straight-forward functions).

How can I do it with a viable (time-effective) algorithm?

Thanks!

Answer 1

[Walter Roberson]

Use fmincon. Make the objective f1^2 and use a nonlinear equality constraint with f2.

[mahdi Izadi]

Thanks!

The problem is that f_1 returns a vector;

i.e. and matlab returns the error

Supplied objective function must return a scalar value. Indeed I am trying to solve n equations simulateneously and the sum of a function of answers should be one.

Could you please kindly let me know how can I fix this?

Thanks so much

[Walter Roberson]

norm(f1(a))

[mahdi Izadi]

Dear Walter;

Thanks so much;

Your suggestion makes the work done;

However the algorithm is excrucietinly slow. (My vector has 100 of elements,) It takes 130 seconds roughly and the problem is that it is inside a loop that should work for more that 1000 iterations...

Is it possible to expedite this solver? I tried a better initial guess and it didn't work. I also tried different algorithms , SQP, iterative, ... but no improvement made in the speed.

Best regards

Mahdi

[Walter Roberson]

It depends what the calculations do. In particular, are there analytic forms of the jacobian? Possibly a sparse form? fmincon needs to estimate the gradient of every variable against every other variable, and if you have hundreds of variables that can get slow.

Answer 2

[Matt J]

You have two equations so, as long as numel(a)=2 and f1 and f2 are differentiable, you can use fsolve. If numel(a)>2 then you have more unknowns than equations and the problem is ill-posed.

[mahdi Izadi]

Dear Matt;

Thanks;

I believe I explained a bit unclear. The problem is somehow OK, as I think the solution proposed above adressed this problem.