scholarly journals A note on the split rank of intersection cuts

2009 ◽  
Vol 130 (1) ◽  
pp. 107-124 ◽  
Author(s):  
Santanu S. Dey
Keyword(s):  
Intersection Cuts ◽  
Split Rank

scholarly journals Intersection Cuts with Infinite Split Rank

2012 ◽  
Vol 37 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Amitabh Basu ◽  
Gérard Cornuéjols ◽  
François Margot
Keyword(s):  
Intersection Cuts ◽  
Split Rank

Multirow Intersection Cuts Based on the Infinity Norm

2021 ◽  
Author(s):  
Álinson S. Xavier ◽  
Ricardo Fukasawa ◽  
Laurent Poirrier
Keyword(s):  
Optimization Problems ◽  
Valid Inequalities ◽  
Linear Optimization ◽  
Computational Cost ◽  
General Purpose ◽  
Mixed Integer ◽  
Infinity Norm ◽  
Intersection Cuts ◽  
Linear Optimization Problems ◽  
Mixed Integer Linear Optimization

When generating multirow intersection cuts for mixed-integer linear optimization problems, an important practical question is deciding which intersection cuts to use. Even when restricted to cuts that are facet defining for the corner relaxation, the number of potential candidates is still very large, especially for instances of large size. In this paper, we introduce a subset of intersection cuts based on the infinity norm that is very small, works for relaxations having arbitrary number of rows and, unlike many subclasses studied in the literature, takes into account the entire data from the simplex tableau. We describe an algorithm for generating these inequalities and run extensive computational experiments in order to evaluate their practical effectiveness in real-world instances. We conclude that this subset of inequalities yields, in terms of gap closure, around 50% of the benefits of using all valid inequalities for the corner relaxation simultaneously, but at a small fraction of the computational cost, and with a very small number of cuts. Summary of Contribution: Cutting planes are one of the most important techniques used by modern mixed-integer linear programming solvers when solving a variety of challenging operations research problems. The paper advances the state of the art on general-purpose multirow intersection cuts by proposing a practical and computationally friendly method to generate them.

scholarly journals Corner polyhedron and intersection cuts

2011 ◽  
Vol 16 (2) ◽  
pp. 105-120 ◽  
Author(s):  
Michele Conforti ◽  
Gérard Cornuéjols ◽  
Giacomo Zambelli
Keyword(s):  
Intersection Cuts

scholarly journals The unitary dual of the hermitian quaternionic group of split rank 2

2006 ◽  
Vol 226 (2) ◽  
pp. 353-388 ◽  
Author(s):  
Marcela Hanzer
Keyword(s):  
Unitary Dual ◽  
Rank 2 ◽  
Split Rank

Reverse Split Rank

2014 ◽  
pp. 234-248
Author(s):  
Michele Conforti ◽  
Alberto Del Pia ◽  
Marco Di Summa ◽  
Yuri Faenza
Keyword(s):  
Split Rank

Intersection Cuts and Corner Polyhedra

2014 ◽  
pp. 235-280
Author(s):  
Michele Conforti ◽  
Gérard Cornuéjols ◽  
Giacomo Zambelli
Keyword(s):  
Intersection Cuts ◽  
Corner Polyhedra

scholarly journals Erratum to “Intersection cuts–standard versus restricted” [Discrete Optim. 18 (2015) 189–192] [ ]

2018 ◽  
Vol 28 ◽  
pp. 115
Author(s):  
Egon Balas ◽  
Tamas Kis
Keyword(s):  
Intersection Cuts

scholarly journals K-invariant cusp forms for reductive symmetric spaces of split rank one

2019 ◽  
Vol 31 (2) ◽  
pp. 341-349
Author(s):  
Erik P. van den Ban ◽  
Job J. Kuit ◽  
Henrik Schlichtkrull
Keyword(s):  
Symmetric Spaces ◽  
Discrete Series ◽  
Series Representation ◽  
Compact Subgroup ◽  
Cusp Forms ◽  
Series Representations ◽  
Rank One ◽  
Discrete Series Representations ◽  
Generalized Matrix ◽  
Split Rank

AbstractLet {G/H} be a reductive symmetric space of split rank one and let K be a maximal compact subgroup of G. In a previous article the first two authors introduced a notion of cusp forms for {G/H}. We show that the space of cusp forms coincides with the closure of the space of K-finite generalized matrix coefficients of discrete series representations if and only if there exist no K-spherical discrete series representations. Moreover, we prove that every K-spherical discrete series representation occurs with multiplicity one in the Plancherel decomposition of {G/H}.

scholarly journals Intersection cuts—standard versus restricted

2015 ◽  
Vol 18 ◽  
pp. 189-192 ◽  
Author(s):  
E. Balas ◽  
T. Kis
Keyword(s):  
Intersection Cuts

scholarly journals Split rank and semisimple automorphism groups of $G$-structures

1987 ◽  
Vol 26 (1) ◽  
pp. 169-173 ◽  
Author(s):  
Robert J. Zimmer
Keyword(s):  
Automorphism Groups ◽  
Split Rank
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