Sparse regression and variable selection for large-scale data have been rapidly developed in the past decades. This work focuses on sparse ridge regression, which enforces the sparsity by use of the L0 norm. We first prove that the continuous relaxation of the mixed integer second order conic (MISOC) reformulation using perspective formulation is equivalent to … Read more
We study a multiple-vehicle routing problem with a minimum makespan objective and compatibility constraints. We provide an approximation algorithm and a nearly-matching hardness of approximation result. We also provide computational results on benchmark instances with diverse sizes showing that the proposed algorithm (i) has a good empirical approximation factor, (ii) runs in a short amount … Read more
This paper studies extended formulations for radial cones at vertices of polyhedra, where the radial cone of a polyhedron P at a vertex v of P is the polyhedron defined by the constraints of P that are active at v. Given an extended formulation for P, it is easy to obtain an extended formulation of … Read more
Two nodes of a wireless network may not be able to communicate with each other directly perhaps due to obstacles or insufficient signal strength. This necessitates the use of intermediate nodes to relay information. Often, one designates a (preferably small) subset of them to relay these messages (i.e., to serve as a virtual backbone for … Read more
We analyze the computational complexity of the synthesis problem of decentralized energy systems. This synthesis problem consists of combining various types of energy conversion units and determining their sizing as well as operations in order to meet time-varying energy demands while maximizing an objective function, e.g., the net present value. In this paper, we prove … Read more
We study the following optimization problem over a dynamical system that consists of several linear subsystems: Given a finite set of n-by-n matrices and an n-dimensional vector, find a sequence of K matrices, each chosen from the given set of matrices, to maximize a convex function over the product of the K matrices and the … Read more
The multilinear polytope MP_G of a hypergraph G is the convex hull of a set of binary points satisfying a collection of multilinear equations. We introduce the running-intersection inequalities, a new class of facet-defining inequalities for the multilinear polytope. Accordingly, we define a new polyhedral relaxation of MP_G referred to as the running-intersection relaxation and … Read more
In this research, we consider the unrelated parallel machine scheduling problem with release dates. The goal of this scheduling problem is to find an optimal job assignment with minimal sum of weighted completion times. As it is demonstrated in the present paper, this problem is NP-hard in the strong sense. Albeit the computational complexity, which … Read more
The stable set problem is a fundamental combinatorial optimisation problem, that is known to be very difficult in both theory and practice. Some of the solution algorithms in the literature are based on 0-1 linear programming formulations. We examine an entire family of such formulations, based on so-called clique and nodal inequalities. As well as … Read more
The Minimum Connectivity Inference (MCI) problem represents an NP-hard generalisation of the well-known minimum spanning tree problem and has been studied in different fields of research independently. Let an undirected complete graph and finitely many subsets (clusters) of its vertex set be given. Then, the MCI problem is to find a minimal subset of edges … Read more