5 papers
A new classification method based on Minimum Spanning Trees
Julio González-Díaz, Beatriz Pateiro-López, Iria Rodríguez-Acevedo
Minimum Spanning Trees have been used in unsupervised learning, particularly in clustering tasks, due to their ability to recognize clusters by removing edges that are considered i…
A note on the convergence guarantees of RLT-based algorithms for polynomial optimization
Alejandro Barros-González, Julio González-Díaz, Brais González-Rodríguez +1
This paper identifies and addresses a mathematical oversight in one of the foundational results on the Reformulation-Linearization Technique (RLT) for polynomial optimization. We t…
Bound tightening in lifted formulations: (sub)solver-dependent impact on performance in RLT-based algorithms
Julio González-Díaz, Brais González-Rodríguez, Ignacio Gómez-Casares
In this paper we explore a relevant aspect of the interplay between two core elements of global optimization algorithms for nonconvex nonlinear programming problems, which we belie…
Solving Sparse Mixed-Integer Quadratic Problems: Application to the Unit Commitment Problem with Optimal Power Flow
Ignacio Gómez-Casares, Pietro Belotti, Bissan Ghaddar +1
Mixed-Integer Quadratically Constrained Quadratic Programs (MIQCQP) arise in a variety of applications, particularly in energy, water, and gas systems, where discrete decisions int…
An extension of an RLT-based solver to MINLP polynomial problems
Julio González-Díaz, Brais González-Rodríguez, Iria Rodríguez-Acevedo
In this paper we extend the core branch-and-bound algorithm of an RLT-based solver for continuous polynomial optimization, RAPOSa, to handle mixed-integer problems. We do so by a d…