An optimisation problem is one that can be formulatd as finding the best value of something. The idea of 'best' is captured in the optmisation criterion, for example least distance travelled. In some cases this is simple, for example a comoany wishing to maxmise profit. In others the problem may need to be reformulated, for example, finding the best line between points as one where the sum of the distance between the points and tth line is minimsed. The latter shows tat there may be several pontential ways to cast something as an optimisation problem with slightly diffrent soluions – for the line do we minimise the sum of the absolute distance to the line, the sum of squares of the distance, the sum of the y-direction distances squared, etc.
Even when we want to find a single exact solution, for example a set of variable values that satisfy an equation, we may want to formulate it as an optomisation problem, for example minimising the absolute difference between the two sides of the desired equality, as continuity can help an algorithm to move stepwise towards a solution.