New MIP approach for efficient change-point detection.
problem Offline multiple change-point detection in data streams.
method Mixed-integer programming (MIP) for globally optimal PWL fitting.
result Provable tighter relaxations for segment assignment variables.
This paper uses MIO to select features for kernel SVM classification.
problem Feature selection for kernel SVM classification.
method Mixed-integer optimization (MIO) for feature subset selection.
result The MIO approach can often outperform linear-SVM-based methods in prediction performance.
New conic quadratic formulations improve outlier detection in regression models.
problem Detecting outliers in regression models with corrupted data.
method Deriving stronger second-order conic relaxations without big-M constraints.
result Proposed formulations are significantly faster than existing methods.
This paper concerns a method of selecting a subset of features for a sequential logit model. Tanaka and Nakagawa (2014) proposed a mixed integer quadratic optimization formulation for solving the problem based on a quadratic approximation of the logistic loss function. However, since there is a significant gap between …
This study uses MILP for feature selection in SVM with budget constraint.
problem Feature selection in SVM with a budget constraint.
method Mixed Integer Linear Programming (MILP) formulation with a budget constraint.
result The proposed MILP formulation and procedures efficiently solve the feature selection problem.
Unified approach tackles logical constraints in mixed-integer optimization.
problem Logical constraints in mixed-integer optimization problems.
method Express logical constraints non-linearly, reformulate as convex binary optimization, solve using outer-approximation.
result Solves problems faster and at larger scale than existing methods.
New technique finds globally optimal symbolic equations.
problem Finding globally optimal mathematical expressions.
method Formulated a mixed integer non-linear program (MINLP).
result Guaranteed global optimality in symbolic regression.
Study on the complexity of deep neural networks and their linear regions.
problem Understanding the complexity and structure of deep neural networks.
method Leveraging the dimension of the space defining each linear region, the study presents bounds and methods for counting linear regions.
result Tighter upper and lower bounds for the maximum number of linear regions on rectifier networks, and a method for exact enumeration.
The paper develops mixed-integer formulations for neural networks using partitioning.
problem Optimizing trained ReLU neural networks with balanced model size and tightness.
method Partitioning node inputs into groups, forming the convex hull via disjunctive programming.
result The proposed formulations outperform existing ones, especially with fewer partitions.
A new portfolio optimization model minimizes maximum drawdown, offering faster and more robust solutions.
problem Optimizing portfolios during financial distress, especially during crises.
method Linearization of Markowitz model based on maximum drawdown, with a Mixed-Integer Linear Programming variation.
result 200 times faster solving time with a more profitable and robust solution.
Paper presents a new method for multiclass classification using hyperplane arrangements.
problem Developing efficient multiclass classifiers.
method Mixed integer programming formulations with hyperplane arrangements, kernel trick adaptation, and dimensionality reductions.
result Our proposal outperforms other methods in multiclass classification tasks.
End-to-end pipeline for data-driven decision making in mixed-integer optimization.
problem Data-driven decision making in mixed-integer optimization with uncertainty.
method Exploiting mixed-integer optimization-representability of machine learning methods, characterizing decision trust regions, and ensembling multiple models.
result Framework generates high-quality prescriptions and controls model robustness.
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
Improved clustering with outlier detection using cardinality constraints.
problem Outlier sensitivity and unbalanced clusters in K-means.
method Formulates a joint outlier detection and clustering problem as a mixed-integer linear program (MILP) with cardinality constraints.
result Proves the optimality of solutions under certain conditions.
A new framework improves solving mixed-integer convex problems with binary indicators.
problem Optimizing mixed-integer convex problems with binary indicators controlling continuous variables.
method Coordinate Optimality Reformulation (CORe) framework, incorporating coordinate-wise optimality information.
result CORe reformulations improve branch-and-bound performance, especially in sparse and structured settings.
We propose a faster and more accurate method for learning classification trees.
problem Learning optimal binary classification trees is challenging and slow.
method We introduce a stronger MIP formulation and Benders' decomposition method.
result Our method is 50 times faster and improves out-of-sample performance.
Best-of-∞ improves LLM performance by efficiently allocating inference-time computation.
problem Achieving optimal performance in test-time LLM ensembling with infinite budget.
method Adaptive generation scheme and weighted ensembles of LLMs, formulated as mixed-integer linear program.
result Optimal ensemble weighting improves performance over individual models.
Mixed integer programming identifies critical neurons in neural networks.
problem Identifying neurons critical for network performance and generalization.
method Developed a mixed integer program (MIP) to assign importance scores to neurons, guiding pruning decisions.
result The method identifies multiple 'lucky' sub-networks resulting in optimized architectures that generalize across datasets.
Differentiable cutting-plane layers solve parametric mixed-integer linear optimization problems.
problem Solving parametric mixed-integer linear optimization problems with changing data.
method Introducing cutting-plane layers (CPLs) for differentiable cutting-plane generation.
result The algorithm computes solutions with low integrality gaps and generalizes to unseen instances.
Proposes a method to learn both constraints and objective functions from data.
problem Data-driven inverse optimization for mixed-integer linear programs (MILPs).
method Two-stage approach: first learns constraints, then estimates objective-function weights conditioned on learned constraints.
result Proposes and validates a method for learning both objective functions and constraints from data.
Study integrates reliability constraints into generation planning models.
problem Challenges in integrating reliability constraints with generation planning models.
method Leverages a weighted oblique decision tree (WODT) technique to embed reliability verification constraints.
result Demonstrates effectiveness in achieving reliable and optimal planning solutions.
Proposes a method to select variables for kernel two-sample tests.
problem Determining whether two samples have the same distribution using informative variables.
method A framework based on kernel maximum mean discrepancy (MMD) for selecting a subset of variables.
result The sample size requirements for the three kernels depend on the number of selected variables, not the data dimension.
Identifies a sub-matrix with maximal sum in large data matrices.
problem Finding a rectangular sub-matrix with the highest sum of entries.
method Proposes two algorithms: CP-GC and MILP, leveraging problem characteristics.
result CPGC approach tends to be the fastest to produce a good solution.
New model uses Half-Full/Half-Empty approach for better portfolio selection.
problem Improving portfolio selection through behavioral finance.
method Generalized Half-Full/Half-Empty approach to positive/negative lotteries, developing nonconvex optimization and mixed-integer linear programming models.
result The Half-Full/Half-Empty model outperforms other methods in risk and profitability.
VNA solves large portfolio optimization problems efficiently.
problem Large-scale portfolio optimization under real-world constraints.
method Mapped to Ising-like Hamiltonian and solved with VNA.
result Identifies near-optimal solutions for over 2,000 assets.
ExDBN learns dynamic Bayesian networks using mixed-integer programming.
problem Learning dynamic causal relationships from time series data.
method Score-based learning algorithm using mixed-integer quadratic programming with branch-and-cut method.
result The proposed method produces more accurate results than state-of-the-art approaches.
New MIP algorithms improve sparse classifier learning times.
problem Sparse classifier learning at large scales.
method Developed exact and approximate MIP algorithms for ℓ0-regularized classification. result Significantly improved statistical performance compared to existing methods.
New method learns BN structures from data efficiently.
problem Learning sparse DAG structure of BN from continuous data.
method Consistent second-order conic integer programming with early stopping criterion.
result Near-optimal solutions to medium-size problems within reasonable time.
Machine learning techniques improve SCUC problem solving speed and efficiency.
problem Improving computational performance of SCUC problem solving.
method Predicting redundant constraints, initial feasible solutions, and optimal solution subspaces.
result Significant reduction in problem size and faster solution times.
New method trains Boltzmann machines without supervision.
problem Training unsupervised learning models.
method Mixed binary quadratic feasibility problem formulation.
result Theory validated on XOR patterns.
New AR framework handles missing values for better recourse actions.
problem Existing AR methods fail with missing values, leading to invalid or costly actions.
method Formulates task using multiple imputation and mixed-integer linear optimization.
result Efficacy of new method demonstrated in experiments.
GLIMPS tackles abundant outlier detection in matched subspace detection.
problem Detecting matched subspaces in high-dimensional data with a high proportion of outliers.
method Two-stage approach combining greedy algorithm and mixed integer programming.
result GLIMPS can tolerate over 80% outliers, significantly outperforming state-of-the-art methods.
Global optimization approach for MAP clustering under Gaussian mixtures.
problem Maximum a-posteriori clustering problem under Gaussian mixture model.
method Mixed-integer nonlinear optimization (MINLP) transformed into mixed-integer quadratic program (MIQP).
result Explicit quantification of optimality gap, leading to globally optimal solutions.
BackboneLearn speeds up MIO-based machine learning problems.
problem Scaling mixed-integer optimization problems in machine learning.
method An open-source Python framework for MIO problems with indicator variables.
result Solves MIO problems faster and more accurately than existing methods.
New combinatorial attacks improve BNN robustness.
problem Improving BNN robustness against adversarial attacks.
method Mixed Integer Linear Programming (MILP) and decomposition-based algorithm (IProp).
result IProp outperforms FGSM in BNN robustness.
Holistic GLMs add constraints for better model quality.
problem Improving classical linear regression models.
method Sparsity-inducing, sign-coherence, and linear constraints.
result Holistic GLMs reliably solve GLMs for various responses.
Paper introduces methods to create fair and accurate regression models.
problem Creating fair and accurate regression models.
method Mixed-integer optimization methods, exact formulations, branch-and-bound algorithm, coordinate descent algorithm.
result Developed methods produce fair and accurate models with reduced training times.
Paper solves DAG learning from continuous data using integer programming.
problem Learning optimal DAGs from continuous observational data.
method Formulated as mixed-integer quadratic optimization (MIQO) model with penalties and regularizations.
result LN formulation outperforms existing methods in computational time and optimality.
Paper proves EM algorithm convergence for mixtures of discrete and continuous parameters.
problem Nontrivial convergence analysis for EM algorithms with mixed-integer parameters.
method Introduces conditions for EM convergence in mixed-integer optimization.
result Proves convergence of EM-based sparse Bayesian learning algorithm.
Optimizes routing in decentralized exchanges with gas fees.
problem Routing in decentralized exchanges with fixed gas fees.
method General optimization framework with mixed-integer model, incorporating gas fees.
result Explicit Karush-Kuhn-Tucker system linking prices, fees, and activation.
Paper proposes a novel optimization method for disaggregating smart meter data.
problem Energy disaggregation, inferring appliance-specific energy consumption from aggregate meter data.
method Two-stage optimization approach: first phase uses mixed integer programming, second phase binary quadratic optimization with penalty terms and appliance constraints.
result Proposed method successfully reconstructs appliance signatures, overcoming previous optimization-based methods' limitations.
This paper tackles minimizing clipped convex functions with heuristics and mixed-integer convex programming.
problem Minimizing a sum of clipped convex functions.
method Heuristics and mixed-integer convex programming.
result Heuristics can find good solutions, and the perspective transformation yields tractable lower bounds.
Method constructs confidence regions for linear models with arbitrary predictors.
problem Constructing confidence regions for linear models with non-linear predictors.
method Mixed Integer Linear Programming for constraints.
result Empty confidence regions for hypothesis testing.
New algorithms improve neural network verification by exploiting piecewise linear structure.
problem Efficiently verify the correctness of neural networks, especially those with high-dimensional inputs.
method Branch-and-Bound (BaB) framework applied to Mixed Integer Linear Programming (MIP) formulation.
result Significant performance improvements and new branching strategies for neural networks.
Mixed-integer programming solves systemic risk measures for interdependent financial systems.
problem Computing systemic risk measures for interdependent financial systems with joint risk considerations.
method Proposes a mixed-integer programming problem to compute clearing vectors in a Rogers-Veraart network model with unrestricted sign operating cash flows.
result The proposed mixed-integer programming problem can compute systemic risk measures for interdependent financial systems.
New method optimizes mixed integer optimization for hierarchical modeling of clustered and longitudinal data.
problem Optimizing subset selection in hierarchical models with clustered and longitudinal data.
method Distribution-free mixed-integer optimization approach for cluster-aware regression.
result The method efficiently solves problems within minutes and outperforms traditional models in generating sparse solutions with high predictive power.
This study proposes a graph partitioning method to improve spatial prediction models.
problem Improving interpretability of spatial prediction models in industries.
method Graph partitioning problem to minimize within-segment variances, formulated as mixed-integer quadratic programming.
result Approximation scheme efficiently identifies spatial segments, improving computational efficiency.
In this paper we propose an approach to preference elicitation that is suitable to large configuration spaces beyond the reach of existing state-of-the-art approaches. Our setwise max-margin method can be viewed as a generalization of max-margin learning to sets, and can produce a set of "diverse" items that can be use…