How can I maximize my output through a "blackbox" function?

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Let's say I have 7 independent variables (inputs) and 1 dependent variable (output). I don't know the function that relates the inputs to the output. All I can do is define each variable, and the "blackbox" will spit out an output. As you can imagine, there are infinite amounts of combinations, and I can't enter each combination to find the greatest result. Is there a good method where I can determine the appropriate inputs that will give me the absolute maximum output?