An affine arithmetic (AA) method is proposed in this paper to solve the optimal power flow
(OPF) problem with uncertain generation sources. In the AA-based OPF problem, all the …

IBEX is an open-source C++ library for constraint processing over real numbers. It provides
reliable algorithms for handling non-linear constraints. In particular, roundoff errors are also …

Interval Taylor has been proposed in the sixties by the interval analysis community for
relaxing continuous non-convex constraint systems. However, it generally produces a non …

We introduce a novel directional multidimensional Hilbert transform and use it to define the
complex-valued analytic image associated with a real-valued image. The analytic image …

Researchers from interval analysis and constraint (logic) programming communities have
studied intervals for their ability to manage infinite solution sets of numerical constraint …

In deterministic continuous constrained global optimization, upper bounding the objective
function generally resorts to local minimization at several nodes/iterations of the branch and …

Tight convex and concave relaxations are of high importance in deterministic global
optimization. We present a method to tighten relaxations obtained by the McCormick …

Structural identification has received increased attention over recent years for performance-
based structural assessment and health monitoring. Recently, an approach for formulating …

We present in this article new strategies for selecting nodes in interval Branch and Bound
algorithms for constrained global optimization. For a minimization problem the standard best …

We say that a convex relaxation of a function is anchored at a particular point in their
domains if the values of the function and the relaxation at this point are equal. The opposite …