# Least mean square optimization problem

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I have the following code for least mean square solution for AF:

thetaDeg = 0:57;

theta = thetaDeg*pi/180;

N = 16;

lambda = 0.1;

dy = 0.5*lambda;

n = 1:N;

yn = (n - 0.5*(N+1))*dy;

AF = [0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.63 0.57 0.29 0.23 0.20 0.17 0.15 0.14 0.12 0.11 0.10 0.10 0.09 0.09 0.08 0.08 0.07 0.07 0.07 0.06 0.06 0.06 0.06 0.00 0.00 0.00];

A = exp(2*pi*1j/lambda*sin(theta')*yn);

w = A \ fliplr(AF)';

How can I impose that the elements of w be of unit magnitude. ie abs(w(i)) = 1. for all i.

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### Answers (3)

Greig
on 28 Apr 2015

##### 1 Comment

John D'Errico
on 28 Apr 2015

No. This is NOT correct at all.

Fmincon cannot handle that class of constraint, since that makes the problem a solve over a finite discrete set. Constraining W to be integers in the set [-1,1] is a nonlinear integer programming problem.

John D'Errico
on 28 Apr 2015

This is a nonlinear integer programming problem. The optimization toolbox does not yet have a tool to solve that class of problem.

I think you will find it solvable by the genetic algorithms toolbox though. You can also find fminconset.m on the file exchange, which does allow the parameters to be defined as discrete parameters.

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Vinod
on 29 Apr 2015

Edited: Vinod
on 29 Apr 2015

##### 1 Comment

Torsten
on 29 Apr 2015

I don't think that it's an integer programming problem. The w_i's are complex, I guess. Thus the optimization is over {x^2+y^2=1}.

Could you post your Problem in a mathematical notation, not in MATLAB code ?

I mean could you specify f in

minimize f(w1,...,wn) s.t. |wi| = 1

?

Best wishes

Torsten.

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