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Theoretical challenges towards cutting-plane selection (Q1650776)

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English	Theoretical challenges towards cutting-plane selection	scientific article

Statements

scholarly article

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Theoretical challenges towards cutting-plane selection (English)

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Mathematical Programming. Series A. Series B

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publication date

13 July 2018

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full work available at URL

https://arxiv.org/abs/1805.02782

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describes a project that uses

cutgeneratingfunctionology

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infinite group relaxation

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MaRDI profile type

MaRDI publication profile

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Some lower bounds on sparse outer approximations of polytopes

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Conflict analysis in mixed integer programming

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SCIP: solving constraint integer programs

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The M{\texttt{CF}}-separator: Detecting and exploiting multi-commodity flow structures in MIPs

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Lifting two-integer knapsack inequalities

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A Machine Learning-Based Approximation of Strong Branching

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Coordinated cutting plane generation via multi-objective separation

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Reduce-and-Split Cuts: Improving the Performance of Mixed-Integer Gomory Cuts

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Split closure and intersection cuts

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Inequalities from Two Rows of a Simplex Tableau

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Embedding {0, ½}-Cuts in a Branch-and-Cut Framework: A Computational Study

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Cyclic group and knapsack facets

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On the facets of the mixed-integer knapsack polyhedron

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Sequence Independent Lifting for Mixed-Integer Programming

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Mingling: mixed-integer rounding with bounds

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Path Cover and Path Pack Inequalities for the Capacitated Fixed-Charge Network Flow Problem

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Conflict graphs in solving integer programming problems

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A Comprehensive Analysis of Polyhedral Lift-and-Project Methods

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Reduced first-level representations via the reformulation-linearization technique: Results, counterexamples, and computations

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Lifting properties of maximal lattice-free polyhedra

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Approximation of corner polyhedra with families of intersection cuts

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On the relative strength of families of intersection cuts arising from pairs of tableau constraints in mixed integer programs

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Intersection Cuts—A New Type of Cutting Planes for Integer Programming

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Facets of the knapsack polytope

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Disjunctive Programming

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New Variants of Lift-and-Project Cut Generation from the LP Tableau: Open Source Implementation and Testing

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A lift-and-project cutting plane algorithm for mixed 0-1 programs

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Gomory cuts revisited

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Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework

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Strengthening cuts for mixed integer programs

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Generalized intersection cuts and a new cut generating paradigm

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Lift-and-project for mixed 0-1 programming: recent progress

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Facets of the Knapsack Polytope From Minimal Covers

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Experiments with Two-Row Cuts from Degenerate Tableaux

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On the relative strength of split, triangle and quadrilateral cuts

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Maximal Lattice-Free Convex Sets in Linear Subspaces

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A geometric approach to cut-generating functions

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A Probing Algorithm for MINLP with Failure Prediction by SVM

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Unique Minimal Liftings for Simplicial Polytopes

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Intersection Cuts with Infinite Split Rank

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A Probabilistic Analysis of the Strength of the Split and Triangle Closures

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Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. I. The One-Dimensional Case

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Light on the infinite group relaxation. I: Foundations and taxonomy

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The 0-1 knapsack problem with a single continuous variable

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A $(k+1)$-Slope Theorem for the $k$-Dimensional Infinite Group Relaxation

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Minimal cut-generating functions are nearly extreme

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Operations that Preserve the Covering Property of the Lifting Region

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Equivariant perturbation in Gomory and Johnson's infinite group problem. III: Foundations for the \(k\)-dimensional case with applications to \(k=2\)

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A Convergent Duality Theory for Integer Programming

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Cook, Kannan and Schrijver's example revisited

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Subset Algebra Lift Operators for 0-1 Integer Programming

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Strengthened Benders Cuts for Stochastic Integer Programs with Continuous Recourse

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Cutting planes from extended LP formulations

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Global Optimization with Polynomials and the Problem of Moments

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On the Hardest Problem Formulations for the 0/1 Lasserre Hierarchy

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On optimizing over lift-and-project closures

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Learning a classification of mixed-integer quadratic programming problems

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Cut Generation through Binarization

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Using rank-1 lift-and-project closures to generate cuts for 0-1 MIPs, a computational investigation

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Minimal Valid Inequalities for Integer Constraints

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Computing deep facet-defining disjunctive cuts for mixed-integer programming

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\(\{ 0,\frac12\}\)-Chvátal-Gomory cuts

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L-shaped decomposition of two-stage stochastic programs with integer recourse

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The Cutting Plane Method is Polynomial for Perfect Matchings

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Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

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A computational study of the cutting plane tree algorithm for general mixed-integer linear programs

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Computation of the Lasserre Ranks of Some Polytopes

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On cutting-plane proofs in combinatorial optimization

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Edmonds polytopes and a hierarchy of combinatorial problems

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Large sparse numerical optimization

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Cut-Generating Functions and <i>S</i>-Free Sets

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A Geometric Perspective on Lifting

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Integer Programming

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Reverse split rank

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Reverse Chvátal--Gomory Rank

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T-space and cutting planes

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Cutting-plane proofs in polynomial space

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On the Matrix-Cut Rank of Polyhedra

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Numerically Safe Gomory Mixed-Integer Cuts

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Chvátal closures for mixed integer programming problems

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A hybrid branch-and-bound approach for exact rational mixed-integer programming

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Revival of the Gomory cuts in the 1990's

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A Class of Hard Small 0-1 Programs

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A convex-analysis perspective on disjunctive cuts

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Elementary closures for integer programs.

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On the rank of mixed 0,1 polyhedra.

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K-Cuts: A Variation of Gomory Mixed Integer Cuts from the LP Tableau

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On the safety of Gomory cut generators

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How tight is the corner relaxation? Insights gained from the stable set problem

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Composite lifting of group inequalities and an application to two-row mixing inequalities

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A 3-slope theorem for the infinite relaxation in the plane

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Solving Large-Scale Zero-One Linear Programming Problems

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Exponential Lower Bounds on the Lengths of Some Classes of Branch-and-Cut Proofs

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Two dimensional lattice-free cuts and asymmetric disjunctions for mixed-integer polyhedra

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A heuristic to generate rank-1 GMI cuts

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Two-Step MIR Inequalities for Mixed Integer Programs

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Valid inequalities based on simple mixed-integer sets

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On Mixing Inequalities: Rank, Closure, and Cutting-Plane Proofs

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On \(t\)-branch split cuts for mixed-integer programs

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On the relative strength of different generalizations of split cuts

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Computational Experiments with Cross and Crooked Cross Cuts

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On mixed-integer sets with two integer variables

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On convergence in mixed integer programming

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On the Rank of Disjunctive Cuts

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A note on the split rank of intersection cuts

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Experiments with Two Row Tableau Cuts

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Split Rank of Triangle and Quadrilateral Inequalities

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Approximating polyhedra with sparse inequalities

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Facets of Two-Dimensional Infinite Group Problems

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Relations between facets of low- and high-dimensional group problems

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On the extreme inequalities of infinite group problems

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Constrained Infinite Group Relaxations of MIPs

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Two row mixed-integer cuts via lifting

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Computing with Multi-row Gomory Cuts

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Optimizing over the first Chvátal closure

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A relax-and-cut framework for Gomory mixed-integer cuts

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On the exact separation of mixed integer knapsack cuts

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Mod‐2 Cuts Generation Yields the Convex Hull of Bounded Integer Feasible Sets

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Worst-case comparison of valid inequalities for the TSP

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Outline of an algorithm for integer solutions to linear programs

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Some polyhedra related to combinatorial problems

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Some continuous functions related to corner polyhedra

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Some continuous functions related to corner polyhedra, II

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Corner polyhedra and their connection with cutting planes

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Lifted flow cover inequalities for mixed \(0\)-\(1\) integer programs

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Mixing mixed-integer inequalities

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Facet of regular 0–1 polytopes

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A Probabilistic Comparison of Split and Type 1 Triangle Cuts for Two-Row Mixed-Integer Programs

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Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut

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Cutting-plane theory: Algebraic methods

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Minimal inequalities

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On the Group Problem and a Subadditive Approach to Integer Programming

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Characterization of facets for multiple right-hand choice linear programs

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Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition

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Degree-two Inequalities, Clique Facets, and Biperfect Graphs

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An electronic compendium of extreme functions for the Gomory-Johnson infinite group problem

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New computer-based search strategies for extreme functions of the Gomory-Johnson infinite group problem

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On the notions of facets, weak facets, and extreme functions of the Gomory-Johnson Infinite Group problem

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Learning when to use a decomposition

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A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0–1 Programming

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Strengthening Chvátal-Gomory cuts and Gomory fractional cuts

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On Counting Lattice Points and Chvátal-Gomory Cutting Planes

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On learning and branching: a survey

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An algorithm for the separation of two-row cuts

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Cones of Matrices and Set-Functions and 0–1 Optimization

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Cutting planes in integer and mixed integer programming

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Testing cut generators for mixed-integer linear programming

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High degree sum of squares proofs, Bienstock-Zuckerberg hierarchy and CG cuts

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New inequalities for finite and infinite group problems from approximate lifting

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A Strong Dual for Conic Mixed-Integer Programs

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A recursive procedure to generate all cuts for 0-1 mixed integer programs

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A simple finite cutting plane algorithm for integer programs

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A disjunctive cutting plane procedure for general mixed-integer linear programs

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Valid Linear Inequalities for Fixed Charge Problems

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Sparse Matrix Methods in Optimization

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A probabilistic comparison of the strength of split, triangle, and quadrilateral cuts

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On the Rank of Cutting-Plane Proof Systems

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Lower bounds for the Chvàtal-Gomory rank in the 0/1 cube

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Lower bounds for resolution and cutting plane proofs and monotone computations

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Valid inequalities for mips and group polyhedra from approximate liftings

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0/1 Polytopes with Quadratic Chvátal Rank

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Mixed \(n\)-step MIR inequalities: facets for the \(n\)-mixing set

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On Cutting Planes

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The \(C^3\) theorem and a \(D^2\) algorithm for large scale stochastic mixed-integer programming: set convexification

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A Hierarchy of Relaxations between the Continuous and Convex Hull Representations for Zero-One Programming Problems

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A hierarchy of relaxations and convex hull characterizations for mixed- integer zero-one programming problems

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Improving Integrality Gaps via Chvátal-Gomory Rounding

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Valid inequalities for mixed 0-1 programs

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Sparsity of Lift-and-Project Cutting Planes

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On the \(0/1\) knapsack polytope

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Faces for a linear inequality in 0–1 variables

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Submodularity and valid inequalities in capacitated fixed charge networks

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Cut-Generating Functions for Integer Variables

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Lexicography and degeneracy: Can a pure cutting plane algorithm work?

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Lifting the facets of zero–one polytopes

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Finitely Convergent Decomposition Algorithms for Two-Stage Stochastic Pure Integer Programs

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Identifiers

zbMATH Open document ID

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10.1007/s10107-018-1302-4

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1650776

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