Matrix inequalities and convex functions constitute a central theme in modern mathematical analysis, with far‐reaching implications across numerical analysis, optimisation, quantum information, and ...

Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.

The relationship of the large deviation rate, $\psi^\ast(a)$, of the mean of independent and identically distributed random variables to their cumulant generating function, $\psi(\lambda)$, is well ...

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

The goal of this course is to investigate in-depth and to develop expert knowledge in the theory and algorithms for convex optimization. This course will provide a rigorous introduction to the rich ...

The Sum Squares function, also referred to as the Axis Parallel Hyper-Ellipsoid function, has no local minimum except the global one. It is continuous, convex and unimodal. It is shown here in its two ...