Posted: Wed Nov 17, 2004 1:16 pm    Post subject: Finding maximum value of a function using computer

Hi, I tried to find the maximum value of:

Here is the result I got in Maple R5: > evalf(maximize(min((1+a)*(4/3), (1+b-a)*2, (1-b)*2), {a,b}, {a=0..1,b=0..1})); 1.333333333 But clearly it is not the maximum value: > evalf(eval(min((1+a)*4/3, (1+b-a)*2, (1-b)*2), {a=1/6, b=1/5})); 1.555555556 Any ideas? Anyone who knows Matlab or whatever and knows how to solve this problem using your software? Thanks!_________________

Alan

Posted: Wed Nov 17, 2004 11:57 pm    Post subject:

In matlab, by simple brute force (and step size = 0.001):

maxima = 1.7140 where a = 0.2860 and b = 0.1430

Posted: Thu Nov 18, 2004 6:15 pm    Post subject:

Max = 12/7 when a = 2/7 and b = 1/7.

(Using NMaximize[Min[4(a+1)/3, 2(1+b-a), 2(1-b)], {a, b}] in Math’ca 5.)

Posted: Fri Nov 19, 2004 10:23 am    Post subject:

It seems the Matlab solution is suboptimal since it won’t work for a few more variables. I will see if I can obtain a copy of Mathematics and try. Thanks for your info!_________________

Alan