We prove that every semidefinite moment relaxation of a polynomial optimization problem
(POP) with a ball constraint can be reformulated as a semidefinite program involving a …

In recent years, there has been an exploration of innovative electric grid concepts centered
around power routers, devices capable of controlling power flows as desired. One of which …

This thesis deals with the computation of global optima of nonlinear semi-infinite
programming problems. These mathematical programming problems are particularly difficult …

Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow
problems. However, solving large-scale SDP problems requires exploiting sparsity. In this …

The increasing integration of renewable energy sources has a long-lasting impact on the
electrical grid, and the liberalisation of the energy sector has significantly changed its …

Many optimization problems in power transmission networks can be formulated as
polynomial problems with complex variables. A polynomial optimization problem with …

We address the issue of computing a global minimizer of the AC Optimal Power Flow
problem. We introduce valid inequalities to strengthen the Semidefinite Programming …

The optimal power flow (OPF) problem models the generation and distribution of electrical
power through a given network, at a specific point in time. The network, represented by a …

Optimization is a mathematical tool that allows to model and solve problems, in which a
criterion is to be optimized. When the function to be minimized and the constraints that …

In this paper, we consider the Optimal Power Flow (OPF) problem which consists in
determining the power production at each bus of an electric network by minimizing the …