How to use quadprog for this multi-dimension problem?

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dragoon 2015-11-5

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https://ww2.mathworks.cn/matlabcentral/answers/253223-how-to-use-quadprog-for-this-multi-dimension-problem

评论： dragoon 2015-11-5

采纳的回答： Alan Weiss

I am trying to use quadprog.m to solve the following 2 dimensional optimization problem.

where $(x_i,y_i)$ is the data point.

How may I implement this 2 dimensional problem in matlab by quadprog? I can do for 1 dimensional problem, i.e., only with $\alpha_i$. But now I have $\alpha_i$ and $\alpha_i'$, i.e., two sets of unknown.

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Answer 1

Alan Weiss 2015-11-5

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编辑：Alan Weiss 2015-11-5

在 MATLAB Online 中打开

All Optimization Toolbox™ solvers require that you put your control variables into a single vector, typically called x. For your case, I suggest that you set the column vector x to be

x = [alpha;alphaprime];

In other words, just concatenate your two existing column vectors of unknowns into one longer column vector. Given this transformation, it is not too difficult to write matrices H and f to represent your problem in the requisite form

1/2*x'*H*x + f*x

Remember, quadprog minimizes, so if you are looking for a maximum, take the negative of your objective function.

If you cannot figure out how to do it with quadprog, you can always use fmincon.

Alan Weiss

MATLAB mathematical toolbox documentation