Matrix analysis
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
A numerical approach to optimization problems with variational inequality constraints
Mathematical Programming: Series A and B
SIAM Review
Applied numerical linear algebra
Applied numerical linear algebra
Computational Optimization and Applications
Solving quadratic (0,1)-problems by semidefinite programs and cutting planes
Mathematical Programming: Series A and B
Fixing Variables in Semidefinite Relaxations
SIAM Journal on Matrix Analysis and Applications
Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
Mathematics of Operations Research
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Computational Optimization and Applications
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
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The presence of complementarity constraints brings a combinatorial flavour to an optimization problem. A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem. The solution to this relaxation can be used to generate feasible solutions to the complementarity constraints. A quadratic programming problem is solved for each of these feasible solutions and the best resulting solution provides an estimate for the optimal solution to the quadratic program with complementarity constraints. Computational testing of such an approach is described for a problem arising in portfolio optimization.