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I am interested in optimizing a function $f(x)$ but evaluating the function for some $x$ is costly.

Each evaluation of the function takes a time $t$ and I have a total time $T$ in which to attempt to optimize this.

Has there been research into how to optimize a function with time constraints?

I realize that this might be problematic because we usually compare optimization methods by their asymptotic behaviour (as $T$ tends to infinity) and here I'm looking at the non-asymptotic behaviour.

Hugh
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  • Have you consulted literature on simulation based optimization? Are function evaluations fully accurate? Do you know any properties of $f$? – LinAlg Sep 30 '16 at 11:49
  • @LinAlg that's a good idea, I have heard about time restraints which engineers face when using simulation to improve a design. I will take a look at that literature. For my specific application the function evaluations are fully accurate. I know that $f$ is continuous and $f(x) \in (0,1)$ – Hugh Sep 30 '16 at 12:06

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