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We derive linear inequality characterizations for sets of the form conv{(x, q) ∈ R d ×R : q ≥ Q(x), x ∈ R d − int(P)} where Q is convex and differentiable and P ⊂ R d. We show that in several cases our characterization leads to polynomial-time separation algorithms that operate in the original space of variables, in particular when Q is a positive-definite… (More)

We consider an optimization problem of the form min x T Qx + c T x s.t. where P ⊆ R n is a polyhedron defined by m inequalities and Q is general and the µ h ∈ R n and the r h quantities are given; a strongly NP-hard problem. In the case |S| = 1, |K| = 0 and m = 0 one obtains the classical trust-region subproblem which is polynomially solvable, and has been… (More)

This thesis studies methods for tightening relaxations of optimization problems with convex objective values over a nonconvex domain. A class of linear inequalities obtained by lifting easily obtained valid inequalities is introduced, and it is shown that this class of inequalities is sufficient to describe the epigraph of a convex and differentiable… (More)

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