Convex Optimization: From Gradient Descent to Interior Point Methods

The real divide in optimization is convex against nonconvex, and it decides whether you can prove your answer is best or merely hope so. Start by learning to recognise convexity without touching a Hessian. Derive why the safe step size is one over the smoothness constant, and why the condition number governs everything. Pick up duality and the KKT conditions as your certificate. Then add curvature, and see how a log barrier turned constrained problems into something solvable in polynomial time.