Set 1 - Taylor Approximations and Convexity. First- and second-order Taylor approximations of one- and two-variable functions. Proofs of convexity for halfspaces and hyperplanes, convexity checks for several functions, and a study of convex quadratic functions and their level sets.
Set 2 - Gradient Descent and Logistic Regression. Gradient descent with exact and backtracking line search on random convex quadratic problems, showing how the condition number affects convergence. Also classification with l2-regularized logistic regression, solved with GD and checked against
fmincon.
Set 3 - Newton's Method and Projections. Minimization of a log-barrier function using gradient descent and Newton's method with feasibility-aware backtracking, compared against CVX. Newton's method converges quadratically. Also closed-form projections onto a Euclidean ball and a box-type set.
Set 4 - SVMs via Interior Point Method. Convex reformulation of the hard-margin SVM for linearly separable data. It is solved with a barrier (interior point) method using Newton steps with feasibility-aware backtracking, and checked against CVX.