• Welcome to CS.SE! I don't understand your problem. What are you trying to achieve? What is your goal? What are the inputs, and what is the desired output? It sounds like you're trying to maximize some function $f(x_1,\dots,x_n)$, subject to the constraint that $x_1+\dots + x_n=1$. Is that right? If so, what can you tell us about the properties of $f$? Can you give us a formula for $f$? Can you describe its structure or characterize it somehow? Without knowing anything about $f$, it's hard to know what to suggest. – D.W. Jul 1 '17 at 6:15
• Thanks @D.W. The formula for $f$ is dependent on the securities within the input portfolio, as well as their historical performance. – turnt Jul 1 '17 at 17:12
• OK, but that's not really what I was asking. I'm not asking what it depends on; I'm asking how it depends on the inputs $x_1,\dots,x_n$ -- and I was asking how it depends on the weights (which apparently are the values we're free to choose, to make the output as large as possible). Is it continuous? Differentiable? Locally linear? Convex? etc. Also, how large is $n$? (How many input weights are there?) The more information you can give us, the more likely that we can help you. – D.W. Jul 2 '17 at 2:29