7 papers
A new classification method based on Minimum Spanning Trees
Julio González-DÃaz, Beatriz Pateiro-López, Iria RodrÃguez-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-DÃaz, Brais González-RodrÃguez +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…
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…
Bound tightening in lifted formulations: (sub)solver-dependent impact on performance in RLT-based algorithms
Julio González-DÃaz, Brais González-RodrÃguez, 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…
Impact of domain reduction techniques in polynomial optimization: A computational study
Ignacio Gómez-Casares, Brais González-RodrÃguez, Julio González-DÃaz +1
Domain reduction techniques are at the core of any global optimization solver for NLP or MINLP problems. In this paper, we delve into several of these techniques and assess the imp…
An extension of an RLT-based solver to MINLP polynomial problems
Julio González-DÃaz, Brais González-RodrÃguez, Iria RodrÃguez-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…