Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
Computational study of a family of mixed-integer quadratic programming problems
Mathematical Programming: Series A and B
A semidefinite framework for trust region subproblems with applications to large scale minimization
Mathematical Programming: Series A and B
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
On cones of nonnegative quadratic functions
Mathematics of Operations Research
New Results on Quadratic Minimization
SIAM Journal on Optimization
Subset Algebra Lift Operators for 0-1 Integer Programming
SIAM Journal on Optimization
Perspective cuts for a class of convex 0–1 mixed integer programs
Mathematical Programming: Series A and B
Generalized spectral bounds for sparse LDA
ICML '06 Proceedings of the 23rd international conference on Machine learning
SIAM Review
Perspective relaxation of mixed integer nonlinear programs with indicator variables
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
SDP diagonalizations and perspective cuts for a class of nonseparable MIQP
Operations Research Letters
On convex quadratic programs with linear complementarity constraints
Computational Optimization and Applications
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A fundamental difficulty when dealing with a minimization problem given by a nonlinear, convex objective function over a nonconvex feasible region, is that even if we can efficiently optimize over the convex hull of the feasible region, the optimum will likely lie in the interior of a high dimensional face, “far away” from any feasible point, yielding weak bounds. We present theory and implementation for an approach that relies on (a) the S-lemma, a major tool in convex analysis, (b) efficient projection of quadratics to lower dimensional hyperplanes, and (c) efficient computation of combinatorial bounds for the minimum distance from a given point to the feasible set, in the case of several significant optimization problems. On very large examples, we obtain significant lower bound improvements at a small computational cost.