Computation of the Lasserre Ranks of Some Polytopes
Mathematics of Operations Research
Integer Polynomial Optimization in Fixed Dimension
Mathematics of Operations Research
Rank complexity gap for Lovász-Schrijver and Sherali-Adams proof systems
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
A note on the stability number of an orthogonality graph
European Journal of Combinatorics
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Unique games on expanding constraint graphs are easy: extended abstract
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Rank Lower Bounds for the Sherali-Adams Operator
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Improved Approximation Guarantees through Higher Levels of SDP Hierarchies
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Graphical Models, Exponential Families, and Variational Inference
Foundations and Trends® in Machine Learning
Integrality gaps for Sherali-Adams relaxations
Proceedings of the forty-first annual ACM symposium on Theory of computing
Sherali-adams relaxations of the matching polytope
Proceedings of the forty-first annual ACM symposium on Theory of computing
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Optimal Sherali-Adams Gaps from Pairwise Independence
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Public-key cryptography from different assumptions
Proceedings of the forty-second ACM symposium on Theory of computing
Matroid matching: the power of local search
Proceedings of the forty-second ACM symposium on Theory of computing
DRL*: A hierarchy of strong block-decomposable linear relaxations for 0-1 MIPs
Discrete Applied Mathematics
On linear and semidefinite programming relaxations for hypergraph matching
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Breaking the rectangle bound barrier against formula size lower bounds
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Approximating sparsest cut in graphs of bounded treewidth
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Improving integrality gaps via Chvátal-Gomory rounding
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Theta Bodies for Polynomial Ideals
SIAM Journal on Optimization
Knapsack problem with probability constraints
Journal of Global Optimization
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
An iterative scheme for valid polynomial inequality generation in binary polynomial programming
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
Integrality gaps of linear and semi-definite programming relaxations for Knapsack
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Sherali-Adams relaxations and indistinguishability in counting logics
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
Polynomial integrality gaps for strong SDP relaxations of Densest k-subgraph
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Semidefinite bounds for the stability number of a graph via sums of squares of polynomials
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Hypercontractivity, sum-of-squares proofs, and their applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Block-diagonal semidefinite programming hierarchies for 0/1 programming
Operations Research Letters
The equivalence of semidefinite relaxations of polynomial 0-1 and ±1 programs via scaling
Operations Research Letters
Approximate formulations for 0-1 knapsack sets
Operations Research Letters
Note: On the polyhedral lift-and-project methods and the fractional stable set polytope
Discrete Optimization
Intermediate integer programming representations using value disjunctions
Discrete Optimization
Copositive and semidefinite relaxations of the quadratic assignment problem
Discrete Optimization
Tree-width and the Sherali-Adams operator
Discrete Optimization
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
0/1 polytopes with quadratic chvátal rank
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Handelman rank of zero-diagonal quadratic programs over a hypercube and its applications
Journal of Global Optimization
The proof-search problem between bounded-width resolution and bounded-degree semi-algebraic proofs
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
On integrality ratios for asymmetric TSP in the sherali-adams hierarchy
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Journal of Global Optimization
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Sherali and Adams (1990), Lov脙隆sz and Schrijver (1991) and, recently, Lasserre (2001b) have constructed hierarchies of successive linear or semidefinite relaxations of a 0--1 polytopePâ聤聠R n converging toP inn steps. Lasserre's approach uses results about representations of positive polynomials as sums of squares and the dual theory of moments. We present the three methods in a common elementary framework and show that the Lasserre construction provides the tightest relaxations ofP. As an application this gives a direct simple proof for the convergence of the Lasserre's hierarchy. We describe applications to the stable set polytope and to the cut polytope.