 In particular, using the Linear Matrix Inequality framework developed in Fazlyab et. al. (2018), we derive analytically a (discrete) Lyapunov function for a two-parameter family of Nesterov optimization methods, which allows for a complete characterization of their convergence rate.
<fluency>  In particular, using the Linear Matrix Inequality framework developed in Fazlyab et. al. (2018), we derive analytically a (discrete) Lyapunov function for a two-parameter family of Nesterov optimization methods, which allows for a complete characterization of their convergence rate.
 In particular, using the Linear Matrix Inequality framework developed in Fazlyab et. al. (2018), we derive analytically a (discrete) Lyapunov function for a two-parameter family of Nesterov optimization methods, which allows for the complete characterization of their convergence rate.