variable declaration for optimization

hello,

I am writing a code where I need to declare two variables which will be used for optimization in further, i.e,

a,b -----> variable(a=complex, b=real)

x=h1*a^2+h2*b^2+h3;------>h1,h2,h3 are constants

x=objective of optimization problem

what will be the code to declare 'a' and 'b';?

[Walter Roberson]

Are you doing Problem Based Optimization?

[Soumili Sen]

no,solver based...

[Walter Roberson]

You do not define variables for solver based optimization: you define a function that accepts a vector of values.

[Soumili Sen]

okk.. thanks

Answer 1

[Ameer Hamza]

Only specify them as input of function handle. Normal procedure is something like this

h1 = 2;
h2 = 3;
h3 = 1;

x = @(a, b) h1*a^2+h2*b^2+h3;
objFun = @(p) x(p(1),p(2));

MATLAB optimization functions expect that the function handle only accepts one multi-dimensional input. Therefore, we converted 'x' with two scalar inputs to objFun with a single 2-dimensional input vector. Then use an optimization solver, such as fmincon()

sol = fmincon(objFun, rand(2,1))

[Soumili Sen]

Thanks... But what about the complex value of the variable?

[Ameer Hamza]

What do you mean by the complex value of variable? Is one of the variable complex number?

[Soumili Sen]

yes,one veriable is complex number

[Ameer Hamza]

Can you show your optimization problem?

[Soumili Sen]

This is my code-

hr = sqrt ( .5/ 2 ) .* (randn(1)+j*randn(1));

hr = sqrt ( .3/ 2 ) .* (randn(1)+j*randn(1));

n1 = sqrt ( .1/ 2 ) .* (randn(1)+j*randn(1));

constellation = sqrt(1/2)*[1+1i*1 1-1i*1 -1-1i*1 -1+1i*1];

cons_size = size(constellation);

x = constellation(randi([1 4],1,100));

r=@(b) (hr*x+hr1*b+n1); % output ------> b is optimization variable with real value

r1=@(a, b) a*r;------> a is optimization variable with complex value

rr =r1;

rr(1:2:end) = 0; % odd data of the symbol-----> objective

[Ameer Hamza]

The objective function must return a scalar number for the minimization algorithm to work. Instead of code, can you attach an image showing the mathematical formulation of your problem?

[Soumili Sen]

yahh u are right,matlab shows an error like.............. "Supplied objective function must return a scalar value." how I can solve that.

[Ameer Hamza]

Can you show the mathematical formulation of your objective function. Currently I don't understand how is it defined.

[Walter Roberson]

Separate the real part of the complex variables from the imaginary part. Return the norm of the expression.

[Soumili Sen]

Thank you both of you.