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How to solve the optimization using Matlab

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Sobin cc
Sobin cc 2016-1-22
关闭： MATLAB Answer Bot 2021-8-20
How can i solve the following optimization using Matlab optimization tool box?..should i choose fmincon for this?
maximize X = a Y + b Z, where 0<a<=1, 0<b<=1 0<x<=1 and y>0
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Torsten
Torsten 2016-1-22
Since Z is unbounded, the maximum X-value is Infinity (the problem is unbounded).
Best wishes
Torsten.
Sobin cc
Sobin cc 2016-1-22
if we bound x to say 500. how this can be written using fmincon?

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John D'Errico
John D'Errico 2016-1-22
编辑：John D'Errico 2016-1-22
You don't understand. IT IS UNBOUNDED. Set Y to any value you wish. as long as b is positive, then let Z approach infinity. X will be made arbitrarily large.
If, as in a comment I see, you decide to give a limit to x as a maximum... (I can only assume that you meant X, not x since there is no x in the problem.) Still, use of fmincon is a waste of time. Just use grade school algebra and some common sense.
Pick ANY values for a, b, and Y. ANY VALUES. Then we have
X = 500 = a*Y + b*Z
So just solve for Z, as a function of a,b,Y.
Z = (500 - a*Y)/b
Since a and Y are bounded and both quite small, both bounded between 0 and 1, Z will NEVER be negative in that result. NEVER.
There is absolutely no reason to bother using fmincon here. Never forget to use common sense, replacing it with a computational algorithm. If you do, you will too often get garbage for results, and you won't know when to trust those results.

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