A Basic Guide to Optimisation

Often problems occur where we want to maximise or minimise some quantity. This is pretty easy to do for simple functions or graphs that we can plot. When the information is plotted in a graph we can visually look for the point in the graph which is highest or lowest. Alternatively if we have a function that can be written mathematically we can use differentiation to find its maximum or minimum.

What optimisation is able to cope with is finding the maximum or minimum of a quantity given that it is limited or `constrained’ by some other facts. Think of trying to build as many products in a factory as you can, whilst only having a limited amount of raw materials and workers both of which need to be used to build the product.

Maximisation or Minimisation?

Normally we want to deal with either a maximisation or minimisation problem. It turns out that these two problems are in fact two sides of the same coin: finding the minimum of some function f(x) is the same as finding the maximum of -f(x). As a result we typically define optimisation problems in the form of a minimisation problem.

\min f(x) = \max -f(x)

Image result for y=x^2 vs y=-x^2

Source: ltcconline

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