How to solve the optimization using Matlab

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

[Torsten]

Why do you restrict the outcome of your objective function (x) to 1 if you want to maximize x ?? (I guess that x and X as well as y and Y are the same ?)

What is Z ?

Best wishes

Torsten.

[Sobin cc]

sorry sir.. its my mistake. it is not X, its y only maximize X = a Y + b Z, where 0<a<=1, 0<b<=1 0<Y<=1 and Z>0

[Torsten]

Since Z is unbounded, the maximum X-value is Infinity (the problem is unbounded).

Best wishes

Torsten.

[Sobin cc]

if we bound x to say 500. how this can be written using fmincon?

Answer 1

[John D'Errico]

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.