Title
On nonlinear constrained minimization problems involving disjunctive constraints
Abstract
We focus on nonlinear minimization problems whose only combinatorial aspect comes from their disjunctive constraints. The recently introduced continuous quadrant penalty formulation of logical disjunctive constraints constitutes a continuous-optimization alternative to the classical formulations (such as the bigM formulation) based on the introduction of binary variables. Such a formulation, based on the introduction of a smooth piecewise-quadratic penalty function, yields to a continuous nonconvex problem. We build on this problem, to derive an efficient computation of upper bounds to be used within Branch-and-Bound-based multi-step approaches. We apply the proposed approach to problems from very different application domains, respectively from discrete geometry and from air traffic management optimization, showing that it is effective at speeding up the computational convergence.
Bio
Sonia Cafieri is Professor at École Nationale de l’Aviation Civile, University of Toulouse, France, where she heads the research group “Mathematical Optimization and Operations Research”. She held positions at École Polytechnique in Paris (collaborating with GERAD in Montréal), at University of Naples and University of Foggia (Italy). She received her PhD in Mathematics from University of Naples in 2006, and her Habilitation from University of Toulouse in 2012. She sits on the Managing Board of the European research group on continuous optimization EUROPT since 2014, and co-leads the French nonlinear mathematical optimization group. She is associate editor of International Transactions in Operational Research.
Her research interests include nonlinear continuous and mixed-integer optimization, with applications arising in particular in air transportation.