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Optimization of 4 cost functions altogether with specified constraints

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Ali Rezaei
Ali Rezaei 2013-6-20
How can I optimize 4 simple cost functions altogether with specified constraints on each of them using MATLAB and optimization toolbox?
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Matt J
Matt J 2013-6-21
编辑：Matt J 2013-6-21
Maybe I wasn't clear. Do you mean you want to calculate
[argmin(f1), argmin(f2), argmin(f3), argmin(f4)]
without using a for-loop? If instead, you're looking for a single x that simultaneously minimizes f1(x), f2(x), f3(x), and f4(x), then see Jan's Answer.
Ali Rezaei
Ali Rezaei 2013-6-23
Yes, that is true. Each f_i (i=1,2,3,4) can be shown as f_i(x1,x2,x3,x4). The x1, x2, x3 and x4 are the same for all of 4 functions.

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Jan
Jan 2013-6-21
编辑：Jan 2013-6-21
You cannot optimize for 4 different criteria at the same time. An optimization requires a scalar cost function, and this is related to the nature of the term "optimimum".
If you want to consider 4 parameters, you still need a norm to create a scalar: E.g. a weighted or unweighted sum(), max() or mean(). Using max() is not smooth anymore and the optimization method need to consider this explicitly.
Example:
Find the price of an article, which maximizes the income of the sellers and minimizes the costs for the buyers simultaneously.
This must fail for obvious reasons.

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