What is the most appropriate machine learning approach for this scenario? The scenario is pretty simple, and I'm sure it's been done a million times. The problem is i don't know the terminology to find the correct resources on the web.

Scenario: I have an environment that can be described in terms of 5 parameters, including and input value A and an output  variable B. There is a dataset containing 100 rows and values for each parameter.

The output B depends on A as well as the remaining environmental variables.

The goal is to find the best value for the input A such that the output B is minimised.

What does the solution for this problem look like? Is it  Machine learning, neural networks, a mathematical optimisation problem? How is this best approached? 

Extension: if I didn't have a dataset in practice,  how would I train a system to suggest different values for A until a minimum is reached? Can neural networks be applied here? Or are we talking about a looping procedure that does known maths in each operation until the output doesn't change much anymore.

I though the generalisation would make it more difficult to answer.
What I am describing is a number of temperature/humidity measure measurements for both inside my house and outside. The input that I can control is the fan speed setting on my evaporative aircon and the output is the loubge temperature which I want to minimise.

During sample gathering, I don't care much about the output. The set of 100 values was arbitrary and more (and diverse) samples can be obtained.

The range of A is a fan speed with discrete values 1-6.
Humidity is a percentage and temperature is 20-45 degrees.
This certainly looks like a basic optimization problem. However, looking from the Machine Learning perspective, what you describe can be framed as a multilabel classification. In that case, you treat the values of A and B as your input, and try to predict the values of those five parameters, which you mentioned:

A, B -> x1, x2, x3, x4, x5

The only pitfall is that 100 records can be insufficient to train a proper classification model, but if you can obtain more training data, this approach seems solid to me.