Mathematics and Optimization
From gradients to variations: stationarity, constraints, and discretization
A common perturbation viewpoint connects zero gradients, Euler–Lagrange equations, KKT conditions, and Galerkin discretization.
When an iteration comes full circle: counterexamples for three-block ADMM
An algorithm can keep moving without approaching a solution. Two periodic orbits illustrate how a numerical observation can become a precise mathematical counterexample.