Before revision:  This approach leads to a convex optimisation problemand it is numerically solved ] via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm  .
After revision:  This approach leads to a convex optimisation problemand it is numerically solved ] via an augmented Lagrangian method and the alternative direction method of multipliers (ADMM) algorithm . The solution effectively reconstructs the dynamic of the asset price between the two dates by recovering the optimal local volatility function, without requiring any time interpolation of the option prices .