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Andrés Gómez

Publications and source records attributed to Andrés Gómez.

47 records · Page 3Linked to original sources
arXiv2023

Outlier detection in regression: conic quadratic formulations

In many applications, when building linear regression models, it is important to account for the presence of outliers, i.e., corrupted input data points. Such problems can be formulated as mixed-integer optimization problems involving cubic terms, each given by the product of a binary variable and a quadratic term of the continuous variables. Existing approaches in the literature, typically relying on the linearization of the cubic terms using big-M constraints, suffer from weak relaxation and poor performance in practice. In this work we derive stronger second-order conic relaxations that do not involve big-M constraints. Our computational experiments indicate that the proposed formulations are several orders-of-magnitude faster than existing big-M formulations in the literature for this problem.

math.OC↗
arXiv2022

On the convex hull of convex quadratic optimization problems with indicators

We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic number of additional variables consists of a single positive semidefinite constraint (explicitly stated) and linear constraints. In particular, convexification of this class of problems reduces to describing a polyhedral set in an extended formulation. While the vertex representation of this polyhedral set is exponential and an explicit linear inequality description may not be readily available in general, we derive a compact mixed-integer linear formulation whose solutions coincide with the vertices of the polyhedral set. We also give descriptions in the original space of variables: we provide a description based on an infinite number of conic-quadratic inequalities, which are ``finitely generated." In particular, it is possible to characterize whether a given inequality is necessary to describe the convex hull. The new theory presented here unifies several previously established results, and paves the way toward utilizing polyhedral methods to analyze the convex hull of mixed-integer nonlinear sets.

math.OC↗
arXiv2022

Hermitian Matrix Definiteness from Quantum Phase Estimation

An algorithm to classify a general Hermitian matrix according to its signature (positive semi-definite, negative or indefinite) is presented. It builds on the Quantum Phase Estimation algorithm, which stores the sign of the eigenvalues of a Hermitian matrix in one ancillary qubit. The signature of the matrix is extracted from the mean value of a spin operator in this single ancillary qubit. The algorithm is probabilistic, but it shows good performance, achieving 97% of correct classifications with few qubits. The computational cost scales comparably to the classical one in the case of a generic matrix, but improves significantly for restricted classes of matrices like $k$-local or sparse hamiltonians.

quant-ph↗
arXiv2021

A Graph-based Decomposition Method for Convex Quadratic Optimization with Indicators

In this paper, we consider convex quadratic optimization problems with indicator variables when the matrix $Q$ defining the quadratic term in the objective is sparse. We use a graphical representation of the support of $Q$, and show that if this graph is a path, then we can solve the associated problem in polynomial time. This enables us to construct a compact extended formulation for the closure of the convex hull of the epigraph of the mixed-integer convex problem. Furthermore, we propose a novel decomposition method for general (sparse) $Q$, which leverages the efficient algorithm for the path case. Our computational experiments demonstrate the effectiveness of the proposed method compared to state-of-the-art mixed-integer optimization solvers.

math.OC↗
arXiv2021

Quantum Arithmetic for Directly Embedded Arrays

We describe a general-purpose framework to design quantum algorithms relying upon an efficient handling of arrays. The corner-stone of the framework is the direct embedding of information into quantum amplitudes, thus avoiding the need to deal with square roots or encode the information in registers. We discuss the entire pipeline, from data loading to information extraction. Particular attention is devoted to the definition of an efficient tool-kit of quantum arithmetic operations on arrays. We comment on strong and weak points of the proposed manipulations, especially in relation to an effective exploitation of quantum parallelism. Eventually, we give explicit examples regarding the manipulation of generic oracles.

quant-ph↗
arXiv2021

Dynamic and Static Object Detection Considering Fusion Regions and Point-wise Features

Object detection is a critical problem for the safe interaction between autonomous vehicles and road users. Deep-learning methodologies allowed the development of object detection approaches with better performance. However, there is still the challenge to obtain more characteristics from the objects detected in real-time. The main reason is that more information from the environment's objects can improve the autonomous vehicle capacity to face different urban situations. This paper proposes a new approach to detect static and dynamic objects in front of an autonomous vehicle. Our approach can also get other characteristics from the objects detected, like their position, velocity, and heading. We develop our proposal fusing results of the environment's interpretations achieved of YoloV3 and a Bayesian filter. To demonstrate our proposal's performance, we asses it through a benchmark dataset and real-world data obtained from an autonomous platform. We compared the results achieved with another approach.

cs.CV↗
arXiv2021

The Axial Anomaly in Lorentz Violating Theories: Towards the Electromagnetic Response of Weakly Tilted Weyl Semimetals

Using the path integral formulation in Euclidean space, we extended the calculation of the abelian chiral anomalies in the case of Lorentz violating theories by considering a new fermionic correction term provided by the standard model extension, which arises in the continuous Hamiltonian of a weakly tilted Weyl semimetal, and whose cones have opposite tilting. We found that this anomaly is insensitive to the tilting parameter, retaining its well-known covariant form. This independence on the Lorentz violating parameters is consistent with other findings reported in the literature. The initially imposed gauge invariant regularization was consistently recovered at the end of the calculation by the appearance of highly non-trivial combinations of the covariant derivatives, which ultimately managed to give only terms containing the electromagnetic tensor. We emphasize that the value of the anomaly with an arbitrary parameter is not automatically related to the effective action describing the electromagnetic response of such materials

cond-mat.mes-hall↗
arXiv2020

Safe Screening Rules for $\ell_0$-Regression

We give safe screening rules to eliminate variables from regression with $\ell_0$ regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the $\ell_0$ optimization problem. Thus, they can be used in a preprocessing step to safely remove variables from consideration apriori. Numerical experiments on real and synthetic data indicate that, on average, 76\% of the variables can be fixed to their optimal values, hence, reducing the computational burden for optimization substantially. Therefore, the proposed fast and effective screening rules extend the scope of algorithms for $\ell_0$-regression to larger data sets.

stat.ML↗
arXiv2020

2x2 convexifications for convex quadratic optimization with indicator variables

In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the bivariate case as a building block, we derive an extended SDP relaxation for the general case. This new formulation is stronger than other SDP relaxations proposed in the literature for the problem, including Shor's SDP relaxation, the optimal perspective relaxation as well as the optimal rank-one relaxation. Computational experiments indicate that the proposed formulations are quite effective in reducing the integrality gap of the optimization problems.

math.OC↗
arXiv2018

Tuning oxygen vacancy diffusion through strain in SrTiO$_3$ thin films

Understanding the diffusion of oxygen vacancies in oxides under different external stimuli is crucial for the design of ion-based electronic devices, improve catalytic performance, etc. In this manuscript, using an external electric field produced by an AFM tip, we obtain the room-temperature diffusion coefficient of oxygen-vacancies in thin-films of SrTiO$_3$ under compressive/tensile epitaxial strain. Tensile strain produces a substantial increase of the diffusion coefficient, facilitating the mobility of vacancies through the film. Additionally, the effect of tip bias, pulse time, and temperature on the local concentration of vacancies is investigated. These are important parameters of control in the production and stabilization of non-volatile states in ion-based memresistive devices. Our findings show the key role played by strain for the control of oxygen vacancy migration in thin-film oxides.

cond-mat.mtrl-sci↗