Previous chapters focused primarily on unconstrained optimization problems typical in training many machine learning models. This chapter addresses situations requiring different approaches. You will learn about constrained optimization, where parameters must satisfy specific conditions, covering the theory (Lagrangian duality, KKT conditions) and practical algorithms like projected gradient methods. We will also introduce derivative-free optimization techniques, useful when gradient information is unavailable or unreliable. Finally, we will cover Bayesian optimization as a method for hyperparameter tuning and touch upon optimization strategies relevant to reinforcement learning.