About

Simge Küçükyavuz is the Chair of Industrial Engineering and Management Sciences at Northwestern University, holding the David A. and Karen Richards Sachs Professorship. Her research expertise encompasses mixed-integer programming, large-scale optimization, optimization under uncertainty, network optimization, and their applications. Her work focuses on theoretical and methodological advancements in these areas, with particular application interests in infrastructure systems such as power and computing networks, social networks, statistical learning, supply chain management, and humanitarian logistics. She has contributed to the field through numerous publications and is recognized for her significant impact in optimization and operations research.

Research topics

• Computer Science
• Mathematical optimization
• Mathematics
• Algorithm

Selected publications

• Solving Convex Quadratic Optimization with Indicators Over Structured Graphs

  arXiv (Cornell University) · 2026-03-02

  articleOpen accessSenior author

  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

• Normalization of ReLU Dual for Cut Generation in Stochastic Mixed-Integer Programs

  Open MIND · 2026-02-05

  preprintSenior author

  We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts. While this dual reformulation guarantees convergence with mixed-integer state variables, it admits multiple optimal solutions that can yield weak cuts. To address this issue, we propose normalizing the dual in the extended space to identify solutions that yield stronger cuts. We prove that the resulting normalized cuts are tight and Pareto-optimal in the original state space. We further compare normalization with existing regularization-based approaches for handling dual degeneracy and explain why normalization offers key advantages. In particular, we show that normalization can recover any cut obtained via regularization, whereas the converse does not hold. Computational experiments demonstrate that the proposed approach outperforms existing methods by consistently yielding stronger cuts and reducing solution times on harder instances.

  DOI

• Integer L-shaped and Lagrangian cuts revisited: A unified perspective

  Operations Research Letters · 2026-02-23

  articleSenior author
  PublisherDOI

• Mixed-Integer Programming for a Class of Robust Submodular Maximization Problems

  INFORMS Journal on Optimization · 2026-05-15

  preprintOpen accessSenior author

  We consider robust submodular maximization problems (RSMs), where given a set of m monotone submodular objective functions, the robustness is with respect to the worst-case (scaled) objective function. The model we consider generalizes two variants of robust submodular maximization problems in the literature, depending on the choice of the scaling vector. On the one hand, by using unit scaling, we obtain a usual robust submodular maximization problem. On the other hand, by letting the scaling vector be the optimal objective function of each individual (NP-hard) submodular maximization problem, we obtain a second variant. Although the robust version of the objective is no longer submodular, we reformulate the problem by exploiting the submodularity of each function. We conduct a polyhedral study of the resulting formulation and provide conditions under which the submodular inequalities are facet-defining for a key mixed-integer set. We investigate several strategies for incorporating these inequalities within a delayed cut generation framework to solve the problem exactly. For the second variant, we present an algorithm that yields a feasible solution along with its optimality gap. We apply the proposed methods to a sensor placement optimization problem in water distribution networks, using real-world data sets to demonstrate their effectiveness. Funding: H. H Wu was supported by National Science and Technology Council (Taiwan) [Grants 111-2221-E-A49-079 and 112-2221-E-A49-126-MY2]. S. Kucukyavuz was supported by Office of Naval Research [Grant N00014-22-1-2602].

  PublisherDOI

• Normalization of ReLU Dual for Cut Generation in Stochastic Mixed-Integer Programs

  ArXiv.org · 2026-02-05

  articleOpen accessSenior author

  We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts. While this dual reformulation guarantees convergence with mixed-integer state variables, it admits multiple optimal solutions that can yield weak cuts. To address this issue, we propose normalizing the dual in the extended space to identify solutions that yield stronger cuts. We prove that the resulting normalized cuts are tight and Pareto-optimal in the original state space. We further compare normalization with existing regularization-based approaches for handling dual degeneracy and explain why normalization offers key advantages. In particular, we show that normalization can recover any cut obtained via regularization, whereas the converse does not hold. Computational experiments demonstrate that the proposed approach outperforms existing methods by consistently yielding stronger cuts and reducing solution times on harder instances.

  PublisherOA PDF

• Solving Convex Quadratic Optimization with Indicators Over Structured Graphs

  arXiv (Cornell University) · 2026-03-02

  preprintOpen accessSenior author

  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

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

  Mathematical Programming · 2025-05-02 · 1 citations

  articleOpen accessSenior author

  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

• Integer programming for learning directed acyclic graphs from nonidentifiable Gaussian models

  Biometrika · 2025-01-01

  articleOpen access

  We study the problem of learning directed acyclic graphs from continuous observational data, generated according to a linear Gaussian structural equation model. State-of-the-art structure learning methods for this setting have at least one of the following shortcomings: (i) they cannot provide optimality guarantees and can suffer from learning suboptimal models; (ii) they rely on the stringent assumption that the noise is homoscedastic, and hence the underlying model is fully identifiable. We overcome these shortcomings and develop a computationally efficient mixed-integer programming framework for learning medium-sized problems that accounts for arbitrary heteroscedastic noise. We present an early stopping criterion under which we can terminate the branch-and-bound procedure to achieve an asymptotically optimal solution and establish the consistency of this approximate solution. In addition, we show via numerical experiments that our method outperforms state-of-the-art algorithms and is robust to noise heteroscedasticity, whereas the performance of some competing methods deteriorates under strong violations of the identifiability assumption. The software implementation of our method is available as the Python package micodag.

  PublisherOA PDFDOI

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

  Mathematical Programming · 2025-08-27

  articleOpen accessSenior author

  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

• Polyhedral Analysis of Quadratic Optimization Problems with Stieltjes Matrices and Indicators

  arXiv (Cornell University) · 2024-04-05

  preprintOpen accessSenior author

  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

Frequent coauthors

• Qimeng Yu

  Université de Montréal

  11 shared

• Alper Atamtürk

  10 shared

• Hao-Hsiang Wu

  10 shared

• Fatma Kılınç-Karzan

  Carnegie Mellon University

  10 shared

• Dabeen Lee

  9 shared

• Merve Meraklı

  7 shared

• Andrés Gómez

  University of Southern California

  7 shared

• Linchuan Wei

  7 shared

Awards & honors

• Nelson Student Paper Prize (2026)
• Mixed-Integer Programming (MIP) Workshop Student Poster Priz…
• Nemhauser Student Paper Prize (2023)
• INFORMS Computing Society Student Paper Prize Runner-Up (202…