You will need to guess your alpha value in order to obtain the best possible SP. You might want to start with a value of 0, with a step size of 0.01 or lower if you want higher accuracy, or 0.1 if you want faster computation. Keep in mind that you will need to do this guessing for each segment of the race track, since there is a different alpha value at every row of the matrix.
Interesting problem, and good luck further! 