About

Andrés Gómez is an Associate Professor and Epstein Family Early Career Chair in the Department of Industrial & Systems Engineering at the Viterbi School of Engineering, University of Southern California. He received his B.S. degrees in Mathematics and Computer Science from Universidad de los Andes in Colombia in 2011 and 2012, respectively. He then earned his M.S. and Ph.D. in Industrial Engineering and Operations Research from the University of California Berkeley in 2014 and 2017. After serving as an Assistant Professor in the Department of Industrial Engineering at the University of Pittsburgh from 2017 to 2019, he joined USC in 2019 where he currently holds the rank of Associate Professor. Dr. Gómez's research focuses on developing new theory and tools for challenging optimization problems arising in finance, machine learning, and statistics. His work addresses the limitations of classical optimization tools in handling the demands of modern application domains that require faster, scalable, and more precise algorithms. Specifically, he aims to bridge the gap between solving convex approximations of problems, which are efficient but yield suboptimal solutions, and tackling non-convex problems directly, which are optimal but computationally expensive. His research systematically constructs strong or ideal convex relaxations of difficult problems, enabling high-quality solutions quickly and efficient optimal problem solving. Dr. Gómez's research draws on disciplines including discrete optimization, mixed-integer optimization, and convex optimization.

Research topics

• Artificial Intelligence
• Mathematical optimization
• Computer Science
• Mathematics

Selected publications

• Solving Convex Quadratic Optimization with Indicators Over Structured Graphs

  arXiv (Cornell University) · 2026-03-02

  preprintOpen access

  This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite and exhibits sparsity. We develop an exact parametric dynamic programming algorithm whose computational complexity depends explicitly on the treewidth of the Hessian's support graph, its volume growth, and an appropriate margin parameter. Under suitable structural conditions, the overall complexity scales linearly with the problem dimension. To demonstrate the practical impact of our approach, we introduce a novel framework for joint forecasting and outlier detection by extending exponential smoothing to time series with outliers. Computational experiments on both synthetic and real data sets show that our method significantly outperforms state-of-the-art solvers.

  PublisherDOI

• Solving Convex Quadratic Optimization with Indicators Over Structured Graphs

  arXiv (Cornell University) · 2026-03-02

  articleOpen access

  This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite and exhibits sparsity. We develop an exact parametric dynamic programming algorithm whose computational complexity depends explicitly on the treewidth of the Hessian's support graph, its volume growth, and an appropriate margin parameter. Under suitable structural conditions, the overall complexity scales linearly with the problem dimension. To demonstrate the practical impact of our approach, we introduce a novel framework for joint forecasting and outlier detection by extending exponential smoothing to time series with outliers. Computational experiments on both synthetic and real data sets show that our method significantly outperforms state-of-the-art solvers.

  PublisherOA PDF

• Fair and Accurate Regression: Strong Formulations and Algorithms

  INFORMS Journal on Optimization · 2026-01-07

  articleOpen access

  This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we study the polynomially solvable single-factor and single-observation subproblems as building blocks and derive their closed convex hull descriptions. Strong formulations obtained for the general fair regression problem in this manner are utilized to solve the problem with a branch-and-bound algorithm exactly or as a relaxation to produce fair and accurate models rapidly. Moreover, to handle large-scale instances, we develop a coordinate descent algorithm motivated by the convex-hull representation of the single-factor fair regression problem to improve a given solution efficiently. Numerical experiments conducted on fair least squares and fair logistic regression problems show competitive statistical performance with state-of-the-art methods while significantly reducing training times. Funding: This research was supported, in part, by the National Science Foundation AI Institute for Advances in Optimization [Award 2112533, AFOSR Award FA9550-24-1-0086, and ONR Award N00014-24-1-2149].

  PublisherDOI

• Computation of Least Trimmed Squares: A Branch-and-Bound framework with Hyperplane Arrangement Enhancements

  arXiv (Cornell University) · 2026-04-13

  preprintOpen access

  We study computational aspects of a key problem in robust statistics -- the penalized least trimmed squares (LTS) regression problem, a robust estimator that mitigates the influence of outliers in data by capping residuals with large magnitudes. Although statistically attractive, penalized LTS is NP-hard, and existing mixed-integer optimization (MIO) formulations scale poorly due to weak relaxations and exponential worst-case complexity in the number of observations. We propose a new MIO formulation that embeds hyperplane arrangement logic into a perspective reformulation, explicitly enforcing structural properties of optimal solutions. We show that, if the number of features is fixed, the resulting branch-and-bound tree is of polynomial size in the sample size. Moreover, we develop a tailored branch-and-bound algorithm that uses first-order methods with dual bounds to solve node relaxations efficiently. Computational experiments on synthetic and real datasets demonstrate substantial improvements over existing MIO approaches: on synthetic instances with 5000 samples and 20 features, our tailored solver reaches a 1% gap in 1 minute while competing approaches fail to do so within one hour. These gains enable exact robust regression at significantly larger sample sizes in low-dimensional settings.

  PublisherDOI

• Outlier Detection in Regression: Conic Quadratic Formulations

  INFORMS journal on computing · 2025-12-02

  article1st authorCorresponding

  In many applications, when building linear regression models, it is important to account for the presence of outliers, that is, 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. In addition, we verify that exact solution of the mixed-integer optimization problems can lead to substantially better-quality solutions than simpler relaxations or heuristics commonly used in practice. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work was supported by a public grant as part of the Investissement d’avenir project [Grant ANR-11-LABX-0056-LMH, LabEx LMH]. A. Gómez is supported by the US Air Force Office of Scientific Research [Grant FA9550-22-1-0369]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2025.1215 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2025.1215 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

  PublisherDOI

• Polyhedral analysis of quadratic optimization problems with Stieltjes matrices and indicators

  Mathematical Programming · 2025-08-27

  articleOpen access

  Abstract In this paper, we consider convex quadratic optimization problems with indicators on the continuous variables. In particular, we assume that the Hessian of the quadratic term is a Stieltjes matrix, which naturally appears in sparse graphical inference problems and others. We describe an explicit convex formulation for the problem by studying the Stieltjes polyhedron arising as part of an extended formulation and exploiting the supermodularity of a set function defined on its extreme points. Our computational results confirm that the proposed convex relaxation provides an exact optimal solution and may be an effective alternative, especially for instances with large integrality gaps that are challenging with the standard approaches.

  PublisherOA PDFDOI

• Code and Data Repository for Outlier detection in regression: Conic quadratic formulations

  INFORMS journal on computing · 2025-10-15 · 1 citations

  article1st authorCorresponding

  The goal of this software is to demonstrate the use of mixed-integer conic quadratic formulations to detect outliers in regression problems (closely related to the Least Trimmed Squares problem in statistics). The methods are implemented in Java and rely on commercial solvers Gurobi and Mosek. Executing the code requires a license for these solvers.

  PublisherDOI

• A parametric approach for solving convex quadratic optimization with indicators over trees

  Mathematical Programming · 2025-05-02 · 1 citations

  articleOpen access

  Abstract This paper investigates convex quadratic optimization problems involving n indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix Q defining the quadratic term is positive definite and its sparsity pattern corresponds to the adjacency matrix of a tree graph. We introduce a graph-based dynamic programming algorithm that solves this problem in time and memory complexity of $$\mathcal {O}(n^2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>n</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> . Central to our algorithm is a precise parametric characterization of the cost function across various nodes of the graph corresponding to distinct variables. Our computational experiments conducted on both synthetic and real-world datasets demonstrate the superior performance of our proposed algorithm compared to existing algorithms and state-of-the-art mixed-integer optimization solvers. An important application of our algorithm is in the real-time inference of Gaussian hidden Markov models from data affected by outlier noise. Using a real on-body accelerometer dataset, we solve instances of this problem with over 30,000 variables in under a minute, and its online variant within milliseconds on a standard computer. A Python implementation of our algorithm is available at https://github.com/aareshfb/Tree-Parametric-Algorithm.git .

  PublisherOA PDFDOI

• Stability Regularized Cross-Validation

  arXiv (Cornell University) · 2025-05-11 · 1 citations

  preprintOpen accessSenior author

  We revisit the problem of ensuring strong test set performance via cross-validation, and propose a nested k-fold cross-validation scheme that selects hyperparameters by minimizing a weighted sum of the usual cross-validation metric and an empirical model-stability measure. The weight on the stability term is itself chosen via a nested cross-validation procedure. This reduces the risk of strong validation set performance and poor test set performance due to instability. We benchmark our procedure on a suite of $13$ real-world datasets, and find that, compared to $k$-fold cross-validation over the same hyperparameters, it improves the out-of-sample MSE for sparse ridge regression and CART by $4\%$ and $2\%$ respectively on average, but has no impact on XGBoost. It also reduces the user's out-of-sample disappointment, sometimes significantly. For instance, for sparse ridge regression, the nested k-fold cross-validation error is on average $0.9\%$ lower than the test set error, while the $k$-fold cross-validation error is $21.8\%$ lower than the test error. Thus, for unstable models such as sparse regression and CART, our approach improves test set performance and reduces out-of-sample disappointment.

  PublisherOA PDFDOI

• Rank-one convexification for quadratic optimization problems with step function penalties

  ArXiv.org · 2025-04-23

  preprintOpen access

  We investigate convexification for convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step function. First, we derive the convex hull for the epigraph of a quadratic function defined by a rank-one matrix and step function penalties. Using this rank-one convexification, we develop copositive and semi-definite relaxations for general convex quadratic functions. Leveraging these findings, we construct convex formulations to the support vector machine problem with 0--1 loss and show that they yield robust estimators in settings with anomalies and outliers.

  PublisherOA PDFDOI

Recent grants

• Advancing Fractional Combinatorial Optimization: Computation and Applications

  NSF · $150k · 2018–2021

• Collaborative Research: CIF: Small: Convexification-based Decomposition Methods for Large-Scale Inference in Graphical Models

  NSF · $250k · 2020–2023

Frequent coauthors

• María Carmen Carnero

  University of Lisbon

  33 shared

• Alper Atamtürk

  25 shared

• Shaoning Han

  University of Southern California

  13 shared

• Phebe Vayanos

  8 shared

• Si̇mge Küçükyavuz

  Northwestern University

  7 shared

• Sina Aghaei

  University of Southern California

  7 shared

• Oleg A. Prokopyev

  6 shared

• Jorge E. Mendoza

  HEC Montréal

  5 shared

Education

• Ph.D., Computer Science

  University of Southern California

  2010

• M.S., Computer Science

  University of Southern California

  2006

• B.S., Computer Science

  University of Southern California

  2004

Awards & honors

• Epstein Family Early Career Chair in Industrial and Systems…