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 ...

Let Γ(X) denote the proper, lower semicontinuous, convex functions on a Banach space X, equipped with the completely metrizable topology of uniform convergence of distance functions on bounded sets.

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 ...

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

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In this paper, we aim to find ecient solutions of a multi-objective optimization problem over a linear matrix inequality (LMI in short), in which the objective functions are SOS-convex polynomials. We ...

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 ...