Use the output of a previous calculation as an initial value for the next calculation?

First, I want to calculate the minimum of f(x:a) over x /in X for each value of a=0,0.1,0.2,...

Second, what I do now is to calculate fminsearch of f(x:a) for a=0, then for a=0.1,... But it will take time.

Third, what I would like to do is to use the optimal value of fminsearch of f(x:0) as an initial value for fminsearch of f(x:0.1).

Then, how can one do this?