A bilinear formulation for vector sparsity optimization
Signal Processing
Computational Optimization and Applications
On the asymmetric eigenvalue complementarity problem
Optimization Methods & Software - GLOBAL OPTIMIZATION
Complementary approaches for the computation of the independent number of a graph
MATH'09 Proceedings of the 14th WSEAS International Conference on Applied mathematics
Disjunctive cuts for non-convex mixed integer quadratically constrained programs
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Computational Optimization and Applications
On linear programs with linear complementarity constraints
Journal of Global Optimization
Computational Optimization and Applications
On valid inequalities for quadratic programming with continuous variables and binary indicators
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
GloMIQO: Global mixed-integer quadratic optimizer
Journal of Global Optimization
Exploring smart grid and data center interactions for electric power load balancing
ACM SIGMETRICS Performance Evaluation Review
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Existing global optimization techniques for nonconvex quadratic programming (QP) branch by recursively partitioning the convex feasible set and thus generate an infinite number of branch-and-bound nodes. An open question of theoretical interest is how to develop a finite branch-and-bound algorithm for nonconvex QP. One idea, which guarantees a finite number of branching decisions, is to enforce the first-order Karush-Kuhn-Tucker (KKT) conditions through branching. In addition, such an approach naturally yields linear programming (LP) relaxations at each node. However, the LP relaxations are unbounded, a fact that precludes their use. In this paper, we propose and study semidefinite programming relaxations, which are bounded and hence suitable for use with finite KKT-branching. Computational results demonstrate the practical effectiveness of the method, with a particular highlight being that only a small number of nodes are required.