A Lagrangian Approach to Optimal Randomization (opens in new tab)

We develop an efficient method for solving non-convex constrained optimization problems that are pervasive in economics. The optimal solution to these problems often involves randomization. We employ a Lagrangian framework and prove that the value of the saddle point characterizing the optimal random solution equals the value of the deterministic dual problem. Our algorithm solves this dual via subgradient descent and recovers the optimal ra...