Optimization using lsqnonneg function

I have to find value of x that minimizes norm of|C*exp(x) - d| subject to x >= 0. I am finding the value of exp(x) that minimizes norm of|C*exp(x) - d| using lsqnonneg function of MATLAB and further I am taking logarthmic of exp(x) to find the value of x. Is this a correct approach or is there some other way in MATLAB to do so? I would appreciate suggestions.

[Torsten]

minimize |C*y-(-C*ones(size(C,2))+d)|^2 subject to y>=0.

Solving this problem with lsqnonneg, x=log(y+1) will solve your original problem.

Best wishes

Torsten.

[rihab]

What does this term (-C*ones(size(C,2)) indicate and why is it subtracted?

[Torsten]

exp(x)>=1 for x>=0.

So you will have to solve

min:||C*(x+1)-d||^2 subject to x>=0

Best wishes

Torsten.

[rihab]

Thank you :) In the absence of constraints, will lsqnonneg function of MATLAB still solve the problem?

[Torsten]

You still have the constraint x>=0 ...

Best wishes

Torsten.

[rihab]

But if I wish to solve the problem in absence of constraints, will lsqnonneg give me optimal value of the variable that will minimize the function?

[Torsten]

So which problem do you want to solve then ?

minimize the norm of ||C*exp(x)-d||^2

(without the constraint x>=0) ?

Best wishes

Torsten.

[rihab]

Yes, exactly.

[Torsten]

Then solve

min: ||C*y-d||^2 subject to y>=0

with lsqnonneg. x=log(y) will be the solution of the original problem.

Best wishes

Torsten.

[rihab]

thanks :)