We study stochastic programs where the decision maker cannot observe the distribution of
the exogenous uncertainties but has access to a finite set of independent samples from this …

We consider the analysis of probability distributions through their associated covariance
operators from reproducing kernel Hilbert spaces. We show that the von Neumann entropy …

The matrix logarithm, when applied to Hermitian positive definite matrices, is concave with
respect to the positive semidefinite order. This operator concavity property leads to …

Tunable diode laser absorption spectroscopy (TDLAS) tomography has been widely used
for in situ combustion diagnostics, yielding images of both species concentration and …

Distance measures between quantum states like the trace distance and the fidelity can
naturally be defined by optimizing a classical distance measure over all measurement …

Quantum relative entropies are jointly convex functions of two positive definite matrices that
generalize the Kullback–Leibler divergence and arise naturally in quantum information …

Recently, the second and third authors developed sums of nonnegative circuit polynomials
(SONC) as a new certificate of nonnegativity for real polynomials, which is independent of …

Many quantum information measures can be written as an optimization of the quantum
relative entropy between sets of states. For example, the relative entropy of entanglement of …

Robust Markov decision processes (MDPs) are used for applications of dynamic
optimization in uncertain environments and have been studied extensively. Many of the …

The abbreviations LMI and SOS stand for “linear matrix inequality" and “sum of squares,"
respectively. The cone n,2d of SOS polynomials in n variables of degree at most 2d is known …