Simple Convex Optimization

1 
C_1 = 0.5; C_2 = 0.8; C_3 = 0.4; C_5 = 0.3;

cvx_begin
    variable A
    minimize( (C_1.*(1 - A)).*(2.^(C_2./(1 - A)) - 1) + (C_3.*A).*(2.^(C_4./A) - 1))
    subject to
         0 < A < 1;
 cvx_end

I have the above convex optimization problem but the following error appears.

Error using .* (line 173)
Disciplined convex programming error:
Cannot perform the operation: {positive constant} ./ {real affine}

Error in ./ (line 19)
z = times( x, y, ‘./’ );

I tried to fix it after reading the division rule but still cannot figure out what is wrong

2

Perhaps it’s not quite as simple as you imply.

You will need to use 2 separate exponential cone constraints.

Expression of the form
y*exp(x/y) , with y > 0, will need to be replaced by a new variable z and the constraint
{x,y,z} == exponential(1)

You will need this to be z1 for the expression involving 1-A, in which 1-A will be the y. And z2 for the expression involving A, for which A will be the y. You will need to convert 2^(b/c) to exp(b*log(2)/c)before doing this.

I will let you work through the details so that you learn something.

1 Like
3

Thanks so much for your help.