Dynamic Programming (DP) provides standard algorithms to solve Markov Decision Processes. However, these algorithms generally do not optimize a scalar objective function. In this paper, we draw connection between DP and (constrained) convex optimization. Specifically, we show clear links in the algorithmic structure between three DP schemes and optimization algorithms. We link conservative Policy iteration to Frank-Wolfe, Mirror-Descent Modified Policy Iteration to Mirror Descent, and Politex (Policy Iteration Using Expert Prediction) to Dual Averaging. These abstract DP schemes are representative of a number of (deep) reinforcement learning (RL) algorithms. By highlighting these connections (most of which have been noticed earlier, but in a scattered way), we would like to encourage further studies linking RL and convex optimization, that could lead to the design of new, more efficient, and better understood RL algorithms.