Matrix analysis
Resource allocation problems: algorithmic approaches
Resource allocation problems: algorithmic approaches
Lagrangean methods for 0-1 quadratic problems
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Convex relaxations of (0, 1)-quadratric programming
Mathematics of Operations Research
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
SIAM Review
A lower bound for a constrained quadratic 0-1 minimization problem
Discrete Applied Mathematics
Complementarity and nondegeneracy in semidefinite programming
Mathematical Programming: Series A and B
Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Global Optimality Conditions for Quadratic Optimization Problems with Binary Constraints
SIAM Journal on Optimization
Output-sensitive cell enumeration in hyperplane arrangements
Nordic Journal of Computing
On the gap between the quadratic integer programming problem and its semidefinite relaxation
Mathematical Programming: Series A and B
Using a Mixed Integer Quadratic Programming Solver for the Unconstrained Quadratic 0-1 Problem
Mathematical Programming: Series A and B
The quadratic knapsack problem-a survey
Discrete Applied Mathematics
A Branch and Bound Algorithm for Max-Cut Based on Combining Semidefinite and Polyhedral Relaxations
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
On duality gap in binary quadratic programming
Journal of Global Optimization
On duality gap in binary quadratic programming
Journal of Global Optimization
Tightening a copositive relaxation for standard quadratic optimization problems
Computational Optimization and Applications
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We investigate in this paper the Lagrangian duality properties of linear equality constrained binary quadratic programming. We derive an underestimation of the duality gap between the primal problem and its Lagrangian dual or SDP relaxation, using the distance from the set of binary integer points to certain affine subspace, while the computation of this distance can be achieved by the cell enumeration of hyperplane arrangement. Alternative Lagrangian dual schemes via the exact penalty and the squared norm constraint reformulations are also discussed.