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.
MVRSM optimizes expensive functions with mixed variables, outperforming state-of-the-art methods.
problem Minimizing expensive functions with mixed continuous and integer variables.
method Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) using rectified linear units.
result MVRSM outperforms state-of-the-art methods on synthetic and real-life benchmarks.
Piecewise-linear approximation improves feature selection in logit models.
problem Improving feature subset selection in sequential logit models.
method Applied piecewise-linear approximation to logistic loss function to frame feature selection as a mixed integer linear optimization problem.
result Piecewise-linear approximation found a better subset of features than quadratic approximation.
A new estimator minimizes non-zero coefficients with a budget on feature-residual correlation.
problem Sparse linear model estimation with feature-residual correlation constraints.
method Mixed Integer Linear Optimization (MILO) for certifiably optimal global solutions.
result Discrete Dantzig Selector provides globally optimal solutions faster than existing methods.
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.
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 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.
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.
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.
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.
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.
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.
Proposes an efficient method for ordered counterfactual explanations.
problem Insufficient explanation of perturbation vectors for executing actions.
method Mixed-Integer Linear Optimization (MILP) approach for evaluating and extracting optimal pairs of actions and orders.
result Demonstrated effectiveness of the proposed method on real datasets.
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.
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.
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 optimize neural networks with ReLU activations using sampling.
problem Optimizing trained neural networks with ReLU activations.
method Iterative algorithm and enhanced algorithm using sampling and neighborhood search.
result The methods reduce the initial MIP problem into smaller LP or MIP problems.
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.
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.
Transformers improve solving mixed-integer programs, especially CLSP.
problem Solving Capacitated Lot Sizing Problem (CLSP) with mixed-integer programming.
method Employing transformer models to predict binary variables in CLSP.
result Transformer model outperforms CPLEX and LSTM in solving CLSP.
New algorithm finds best subset in linear regression using MIO.
problem Choosing best subset of features in linear regression.
method Discrete extension of first order optimization methods combined with MIO solver.
result Provably optimal solutions with guarantees on suboptimality.
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.
Graph neural nets learn better branch-and-bound policies.
problem Combinatorial optimization problems, especially hard ones.
method Graph convolutional neural network model trained via imitation learning.
result Improves over state-of-the-art methods and expert-designed rules.
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.
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.
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.
This work analyzes machine learning for Lagrangian Relaxation in MILP.
problem Improving efficiency in solving large-scale MILP problems.
method Data-driven Algorithm Design approach to learn Lagrangian multipliers.
result Stochastic Gradient Ascent achieves the minimax optimal rate for learning multipliers.
ReLU networks trained with MILPs match deep learning accuracy.
problem Training deep neural networks efficiently.
method Iterative training with Mixed Integer Linear Programs (MILPs).
result ReLU networks can be trained with MILPs achieving similar accuracy to deep learning 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.
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.
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 learning-based approach optimizes automated lane changes with mixed-integer optimization and machine learning.
problem Traditional motion planning methods are inefficient and lack generalization capability.
method Mixed-Integer Quadratic Problem (MIQP) for optimal trajectories, supervised learning for fast decision-making.
result The proposed model outperforms existing motion planning methods in optimality, efficiency, and generalization.
The study examines robustness auditing for linear regression, improving existing methods and identifying computational challenges.
problem Detecting small subsets of data that can reverse regression coefficients.
method Empirical study of mixed integer quadratically constrained optimization and exact greedy methods, combined with a spectral algorithm.
result Existing methods largely outperform state of the art, but computational bottlenecks remain, especially for higher dimensions.
A new framework for predictive clustering and optimization.
problem Finding clusters of data that yield low error on a supervised target.
method Generalized optimization framework using MILP and MM for scalability.
result Models can uncover different interpretable discrete cluster structures.
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.
Develops a new method for optimizing with uncertain data.
problem Uncertainty in real-world optimization problems.
method Combines chance constraints and constraint learning for mixed-integer linear optimization.
result Data-driven solution for setting probabilistic bounds on learned constraints.
Algorithm removes units and layers of neural networks without losing accuracy.
problem Deploying large neural networks under limited resources.
method Mixed-Integer Linear Programming (MILP) and L1 regularization.
result Lossless compression of neural networks is achieved.
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.
Optimizes marketing strategies with practical constraints.
problem Adjusting marketing activities with minimum and maximum changes.
method Formulated as a mixed integer nonlinear program (MINLP), reformulated for computational efficiency.
result Significant improvements in solution process for realistic problems.
The paper tackles robust classification trees for distribution shifts, improving accuracy in public health and social work.
problem Learning robust classification trees for high-stakes settings with distribution shifts.
method Mixed-integer robust optimization technology to reformulate as a two-stage linear robust optimization problem.
result Increase of up to 12.48% in worst-case accuracy and 4.85% in average-case accuracy.
Automates model selection for GLMs using optimization.
problem Automating model selection for generalized linear models.
method Mixed-integer conic optimization for feature subset selection and model constraints.
result Optimization of AIC and BIC criteria with multicollinearity constraints.
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.
A hybrid algorithm combines optimization and enumeration for symbolic regression.
problem Finding any function from a set of operators without prior specification.
method Mixed-integer nonlinear optimization with explicit enumeration and constraints.
result The hybrid algorithm is competitive with state-of-the-art methods.
Pipeline-aware hyperparameter tuning speeds up machine learning pipelines by reusing intermediate computations.
problem High computational burden in hyperparameter tuning of multi-stage pipelines.
method Proposes a hybrid hyperparameter tuning method and a caching problem formulated as an ILP to maximize reuse.
result Pipeline-aware approach offers over an order-of-magnitude speedup over independent evaluations.
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.
Polynomial-time algorithm for inferring high-dimensional linear regression from a single sample.
problem Inferring an unknown feature vector from linear measurements in high dimensions without sparsity assumptions.
method Combining PSLQ integer relation detection and LLL lattice basis reduction algorithms.
result Polynomial-time recovery of β∗ from linear measurements Y=Xβ∗, even with one sample. New research limits how deep neural networks can be for certain functions.
problem Understanding the depth required for neural networks to represent specific functions.
method Mixed-integer optimization, polyhedral theory, tropical geometry.
result Neural networks with more than one layer are necessary to represent certain functions.