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I have $m$ functions of $n$ variables, $f_i(x_1,\dots,x_n)$ (where both $m$ and $n$ are finite), and I want to find the maximum (or the minimum) of: \begin{equation} G=\sum_{i=1}^{m}f_i(\bf{x}) \end{equation} Can we say something a priori about the properties of $G$, properties that we can exploit for the optimization? For example, if all the $f_i$ are convex, then $G$ is convex as well, and this may help greatly in solving the problem. The same can be asked for: \begin{equation} H=\prod_{i=1}^{m}f_i(\bf{x}) \end{equation}

Thanks.

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  • $\begingroup$ The sums and products are over m+1 functions. Go from $1$ to $m$, rather than from $0$. The only thing I can suggest is using Lagrange multipliers $\endgroup$
    – Angela Pretorius
    Commented Sep 10, 2012 at 19:55

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