How can I model my objective function for optimization? in quadprog

2018 7 2
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更新时间：2018 7 2
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x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+0.3*x(5)^2+0.3*x(6)^2+0.3*x(7)^2
If someone know please help.
Thank You.

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Alan Weiss
Alan Weiss 2018-7-2

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As the function reference page for quadprog states, the objective function in terms of the matrices H and f is
1/2*x'*H*x + f'*x
You have a 7-dimensional x. So f = ones(7,1) for the first seven terms of your sum. Then you have three terms for quadratic terms. Take
H = spalloc(7,7,3); % Sparse 7-by-7 array with 3 nonzero entries
H(5,5) = 2*0.3;
H(6,6) = 2*0.3;
H(7,7) = 2*0.3;
The reason you multiply those entries by 2 is because of the 1/2 in the definition of the quadprog objective function.
Alan Weiss
MATLAB mathematical toolbox documentation

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NIKET shah
NIKET shah 2018-7-2
thank you.
it would be 4 nonzero entries, instead of three.
and also
can i solve this objective function with the help of quadprog..
{x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+0.3*x(5)^2+0.3*x(6)^2+0.3*x(7)^2)/{x(1)+x(2)+x(3)+x(4)+x(5)+x(6)+x(7)+x(8)+x(9)+0.3*x(5)^2+0.3*x(6)^2+0.3*x(7)^2+0.3*x(7)^2+0.3*x(9)^2).. Can i create a different function file in quadprog.?
Alan Weiss
Alan Weiss 2018-7-2
It looks like you have a quotient of two quadratics there. The answer is no, quadprog does not address a quotient of quadratics. For that, you can use fmincon or fminunc.
Alan Weiss
MATLAB mathematical toolbox documentation
NIKET shah
NIKET shah 2018-7-2
okay. I have used fmincon but it doesn't returns integer argument. like MILP. is there another solver for quadratic objective function.
Alan Weiss
Alan Weiss 2018-7-2
I don't know what you are trying to do exactly. You could look at a Mixed-Integer Quadratic Programming example. There are more examples of this type of problem in Financial Toolbox documentation.
Alan Weiss
MATLAB mathematical toolbox documentation

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