# calibration of local volatility to

I'm looking to understand the practical details of calibrating local volatility to option prices for a range of different expiries using the Dupire local volatility equation. Would appreciate some guidance on the following:

a) Is there a good reference that outlines the key details of local vol calibration? Having never attempted this before, one key confusion I have is whether the calibration is via a global optimisation of $$\sigma(t, S(t)$$ over a range of expiries and strikes, or is there a sequential bootstrap-type of approach that is possible?

b) When implementing the local vol model via MC simulation, how is the resulting $$\sigma(t,S(t))$$ surface used? For example, given a series of expiries, $$T_1,T_2,...,T_N$$, do you simulate from $$T_{i-1}$$ to $$T_i$$ using a forward volatility determined from the $$\sigma(t,S(t))$$ surface, or something else?