Convex optimisation constitutes a fundamental area in applied mathematics where the objective is to identify the minimum of a convex function subject to a set of convex constraints. This framework ...

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

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 ...

Transactions of the American Mathematical Society, Vol. 327, No. 2 (Oct., 1991), pp. 795-813 (19 pages) Let Γ(X) denote the proper, lower semicontinuous, convex functions on a Banach space X, equipped ...

Quantum process tomography is often used to completely characterize an unknown quantum process. However, it may lead to an unphysical process matrix, which will cause the loss of information with ...

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Ф-function technique, a ...

What if the next new mathematical discovery didn’t come from a human mind, but from an AI? Imagine a machine not just crunching numbers but proposing original solutions to problems that have baffled ...