Help with a simple ojective

Hi all,

I have recently started implementing optimization problems using CVX and still learning. I have implemented the following quadratic constraint quadratic optimization problem. However, CVX is producing the error. I have learned from online help available that multiplication of two variables is not allowed in CVX. Could anyone help me with how I can Implement this simple program in CVX?

cvx_begin
variable x(3,1)
minimize((x(1).^2)+(0.1x(2).^2)+(x(3).^2)-(x(1).x(3))-x(2))
subject to
x(1)+x(2)+x(3)-(x(1)^2)-(x(2)^2)-(0.1(x(3).^2))+(0.2x(1).*x(3)) >= 1;
x >= 0;

cvx_end

It is an example from the MOSEK manual and in CVX you have to input it in the same way, that is write each quadratic expression in the standard form x^TQx and then input it as quad_form(x,Q).

Thanks for your response. Michal. Yes, you are right I have taken this example from the manual.
As you suggested, I have tried the following code with CVX but still it’s not working.

close all; clear; clc
n = 3;
H = [2 0 -1; 0 0.2 0; -1 0 2]; % make spsd
f = [0 -1 0]‘;
Q = [-2 0 0.2;0 -2 0;0.2 0 -0.2]; % make spsd
g = [1 1 1]’;
cvx_begin
variable x(n)
minimize(0.5*quad_form(x,H) + f’x)
0.5quad_form(x,Q)+g’*x <=1
x >= 0
cvx_end

Error using cvxprob/newcnstr
Disciplined convex programming error:
Invalid constraint: {concave} <= {real constant}

Error in <= (line 21)
b = newcnstr( evalin( ‘caller’, ‘cvx_problem’, ‘’ ), x, y, ‘<=’ );

Error in quad_example (line 50)
0.5*quad_form(x,Q)+g’*x <=1

I would be grateful if you could give some suggestions to debug this code.

You wrote the inequality the wrong way. It is >=1 and not <=1.

Thanks Michal. It’s perfect now.