I'm trying to find the maximum value of the function $f(x,y)=(ax+by)^p+x^p$ subject to the constraint $x^p+y^p=1$. Here, $a,b$ and $p$ are constants with $a,b>0$ and $p>1$, and $x,y>0$. I have found the maximum in the special case $p=2$ and tried to use Lagrange multipliers in the general case but couldn't success. Any help?
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What is $p$? Do you know $a$ and $b$ or are they unknowns? Is the problem concave? If you know all the values and the problem is concave, I recommend just using a numerical solver like CVX. – Y. S. Jan 06 '15 at 18:45
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The constants a and b are unknowns. What do you mean by a"concave problem" and "CVX"? Thank you. – Amer Jan 06 '15 at 21:16