New model guarantees integer optimal solutions for combinatorial problems.
problem Finding optimal solutions for combinatorial problems with costly or noisy evaluations.
method Developed a surrogate model with integer-valued minima for combinatorial optimization.
result Outperforms other optimization algorithms on specific combinatorial problems.
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.
Paper proposes algorithms for BMF using integer programming.
problem Approximating binary input matrix as product of two smaller binary factors.
method Alternating optimization strategy using integer programming to solve subproblems and combine solutions.
result Proposed algorithms outperform state of the art on medium-scale problems.
Optimizes intervention design for causal discovery using integer programming.
problem Identifying causal structures from observational data due to confounding variables.
method Uses integer programming to design minimal intervention sets for causal structure identifiability.
result Provides exact and modular solutions adaptable to various experimental settings and constraints.
Paper finds instantons for Kapustin-Witten equations on a specific manifold.
problem Existence of solutions to Kapustin-Witten equations on (0,∞)imesR2imesR. method Explains existence of solutions interpolating between two model solutions.
result Interpolation solutions exist with specific label constraints.
We propose a novel high-dimensional linear regression estimator: the Discrete Dantzig Selector, which minimizes the number of nonzero regression coefficients subject to a budget on the maximal absolute correlation between the features and residuals. Motivated by the significant advances in integer optimization over the…
The crosscap number of a knot is an invariant describing the non-orientable surface of smallest genus that the knot bounds. Unlike knot genus (its orientable counterpart), crosscap numbers are difficult to compute and no general algorithm is known. We present three methods for computing crosscap number that offer varyi…
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.
In this article, we consider a gauge-theoretic equation on compact symplectic 6-manifolds, which forms an elliptic system after gauge fixing. This can be thought of as a higher-dimensional analogue of the Seiberg-Witten equation. By using the virtual neighbourhood method by Ruan, we define an integer-valued invariant, …
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.
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.
Given a graphical model, one essential problem is MAP inference, that is, finding the most likely configuration of states according to the model. Although this problem is NP-hard, large instances can be solved in practice. A major open question is to explain why this is true. We give a natural condition under which we …
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.
New algebraic numbers defined by a specific equation.
problem No direct problem stated; focuses on new algebraic numbers.
method Definition of superalgebraic Markov numbers via a Grassmann integer equation.
result Introduced new algebraic numbers with applications in Teichmüller spaces.
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.
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical …
Stochastic cutting planes improve data-driven optimization speed.
problem Data-driven Mixed-Integer Nonlinear Optimization problems.
method Stochastic version of cutting-plane method.
result Stochastic algorithm converges to ε-optimal solution with high probability.
In earlier work, we derived formal matched asymptotic profiles for families of Ricci flow solutions developing Type-II degenerate neckpinches. In the present work, we prove that there do exist Ricci flow solutions that develop singularities modeled on each such profile. In particular, we show that for each positive int…
Improved Compressed Sensing by optimizing sparse solutions with mixed integer programming.
problem Finding sparse solutions to linear measurements with numerical tolerance.
method Introducing an ℓ2 regularized formulation, reformulating as a mixed integer second order cone program, deriving a second order cone relaxation, and developing a custom branch-and-bound algorithm. result Our approach produces solutions that are on average 6.22% more sparse compared to state-of-the-art methods.
The Slope Conjecture relates a quantum knot invariant, (the degree of the colored Jones polynomial of a knot) with a classical one (boundary slopes of incompressible surfaces in the knot complement). The degree of the colored Jones polynomial can be computed by a suitable (almost tight) state sum and the solution of a …
In this paper we study the (asymptotic and exponential) stability of the m-fold circle as a solution of the p-curve shortening flow (p≥1 an integer).
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.
In the last twenty-five years (1990-2014), algorithmic advances in integer optimization combined with hardware improvements have resulted in an astonishing 200 billion factor speedup in solving Mixed Integer Optimization (MIO) problems. We present a MIO approach for solving the classical best subset selection problem o…
New periodic solution found in 4-body problem, not part of expected geometrical family.
problem Finding new periodic solutions in the 4-body problem not fitting the expected geometrical family.
method Analytic continuation of a numerical solution to discover a new family of solutions.
result Existence of a non-planar periodic solution for any pair of masses and integer n.
New method learns DAGs from noisy data without identifiability assumptions.
problem Learning DAGs from non-identifiable Gaussian models with heteroscedastic noise.
method Mixed-integer programming framework for medium-sized problems.
result Asymptotically optimal solution with early stopping criterion.
This dissertation uses ILP to learn Bayesian network structures efficiently.
problem Learning the structure of Bayesian networks from data.
method Integer Linear Programming formulation with cluster constraints and cutting planes.
result The approach finds feasible solutions for Bayesian network structures efficiently.
New solutions found for a complex boundary problem.
problem One-phase free boundary problem in geometry.
method New connection with minimal surfaces.
result Disproved a conjecture and constructed homogeneous solutions.
In the present paper, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. Th…
Unified framework for intersectionally fair AI models using MIO.
problem Bias in AI models for high-risk domains.
method Mixed-Integer Optimization (MIO) for fairness and interpretability.
result Improved performance in detecting and mitigating bias at intersections.
We prove that on a closed surface, for any c>0, our min-max theory for prescribing mean curvature produces a solution given by a curve of constant geodesic curvature c which is almost embedded, except for finitely many points, at which the solution is a stationary junction with integer density. Moreover, each smoot…
Solves the film scheduling and staggered showtimes problem for movie theaters.
problem Maximize attendance and revenue by scheduling films with staggered showtimes.
method Binary integer linear optimization to find optimal schedules for each cluster of neighboring locations.
result Optimal scheduling cannot be done for all locations at once, but must be done for each cluster.
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.
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.
This paper proposes new search algorithms for counterfactual explanations based upon mixed integer programming. We are concerned with complex data in which variables may take any value from a contiguous range or an additional set of discrete states. We propose a novel set of constraints that we refer to as a "mixed pol…
Using Blanchfield pairings, we show that two Alexander polynomials cannot be realized by a pair of matrices with Gordian distance one if a corresponding quadratic equation does not have an integer solution. We also give an example of how our results help in calculating the Gordian distances, algebraic Gordian distances…
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.
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 letter tackles channel assignment in uplink wireless communication systems.
problem Maximizing the sum rate of all users in uplink wireless communication systems with integer channel assignment constraints.
method A convex optimization based algorithm is used to find the optimal channel assignment. Machine learning approaches, including CNNs, FNNs, random forest, and GRUs, are employed to reduce computation time.
result Machine learning methods largely reduce computation time with slightly compromised prediction accuracy.
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.
In this paper we study the classification of ancient convex solutions to the mean curvature flow in Rn+1. An open problem related to the classification of type II singularities is whether a convex translating solution is k-rotationally symmetric for some integer 2≤k≤n, namely whether its level set is a …
Even though the disk embedding theorem is not available in dimension 4 for free fundamental groups, some surgery problems may be shown to have topological solutions. We prove that surgery problems may be solved if one considers closed 4-manifolds and the intersection pairing is extended from the integers, and prove a r…
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.
Paper presents a framework to automatically discover constraints from data.
problem Discovering constraints from data for structured output prediction.
method Formulates structured output prediction as ILP, mines constraints by estimating polytopes of feasible set.
result Successfully identifies feasible sets and constraints for various tasks.
In this study we introduce a new technique for symbolic regression that guarantees global optimality. This is achieved by formulating a mixed integer non-linear program (MINLP) whose solution is a symbolic mathematical expression of minimum complexity that explains the observations. We demonstrate our approach by redis…
New q-deformed integers help compute Jones polynomials efficiently.
problem Computing Jones polynomials of rational links efficiently.
method Defining q-deformed integers from pairs of coprime integers and using them to compute Jones polynomials.
result Efficient algorithm for computing Jones polynomials of rational links.
Optimizes risk assessment tools using mixed-integer programming.
problem Challenges in healthcare risk assessment due to label scarcity and asymmetric misclassification costs.
method Jointly optimizes scoring weights and category thresholds via mixed-integer programming (MIP).
result Prevents label-scarce category collapse and achieves more accurate risk categorization.
The abstract discusses resurgent functions in quantum knot invariants.
problem Understanding the asymptotic expansion of quantum knot invariants.
method Using resurgent functions and q-series to conjecture and compute knot invariants. result Explicit computations match conjectured values for specific knots.