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

A real valued function f defined on a real interval I is called (ε,δ)-convex if it satisfies f(tx+(1-t)y)≤ tf(x)+(1-t)f(y)+ε t(1-t)|x-y|+δ for x,y∈ I,t∈ [0,1]. The main results of the paper offer ...

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 ...

As bond yields rise and fall past certain levels, there are episodes of highly technical yet increasingly familiar flows that can accelerate moves in either direction. Analysts and traders use terms ...

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 ...