This course discusses basic convex analysis (convex sets, functions, and optimization problems), optimization theory (linear, quadratic, semidefinite, and geometric programming; optimality conditions ...

Convex geometry and combinatorial optimisation form a vibrant nexus of research that bridges theoretical mathematics with practical algorithm design. The study of convex sets and their structural ...

where \(\mathsf{G}(\cdot)\) is some convex operator and \(\mathcal{F}\) is as set of feasible input distributions. Examples of such an optimization problem include finding capacity in information ...